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List of Formulas and Statistics Table, Cheat Sheet of Statistics

New York Academy of ArtStatistics

AP statistics formula sheet include mensuration, trigonometry, arithmetic and geometric series, summation, logarithms and exponential, complex number, maclaurin's series and hyperbolic functions

Typology: Cheat Sheet

2021/2022

Uploaded on 02/07/2022

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List MF20
List of Formulae and Statistical Tables
Cambridge Pre-U Mathematics (9794) and
Further Mathematics (9795)
For use from 2017 in all papers for the above syllabuses.
CST317
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Partial preview of the text

Download List of Formulas and Statistics Table and more Cheat Sheet Statistics in PDF only on Docsity!

List MF

List of Formulae and Statistical Tables

Cambridge Pre-U Mathematics (9794) and

Further Mathematics (9795)

For use from 2017 in all papers for the above syllabuses.

CST

PURE MATHEMATICS

Mensuration

Surface area of sphere = 4 πr^2

Area of curved surface of cone = πr × slant height

Trigonometry

a^2 = b^2 + c^2 − 2 bc cos A

Arithmetic series

un = a + ( n − 1) d

Sn = 12 n ( a + l ) = 12 n {2 a + ( n − 1) d }

Geometric series

un = arn^ − 1

Sn =

a r^ n

r

S∞ =

a

r

for r < 1

Summations

2 1 6 1

= ∑ =^ +^ + n r

r n n n

3 1 2 2 4 1

= ∑ =^ + n r

r n n

Binomial series

  +^   = 

   +^   + 

n n n

r r r

( )

+ = + ^ ^ −^ + ^ ^ −^ + + ^  − + +

a b n^ a n^ n^ a n^ b n^ a n^ b n a n^ r^ b r^ bn

r

, ( n ∈ ℕ), where

C

  =^ =

n r

n n

r r n r

( ) ( 1 )^2 ( 1 ...) ( 1 )

+ n^ = + + + + r +

n n n n n r

x nx x x

r

( x < 1, n ∈ ℝ)

Logarithms and exponentials

e x^ ln^ a^ = ax

Complex numbers

{ r (cos θ + i sin θ )} n^ = rn (cos nθ + i sin nθ )

ei θ^ = cos θ + i sin θ

The roots of z n^ = 1 are given by z =

2 i

e

k n π

, for k = 0, 1, 2, ..., n – 1

Trigonometric identities

sin( A ± B ) = sin A cos B ± cos A sin B

cos( A ± B ) = cos A cos B  sin A sin B

tan( A ± B ) =

tan tan

1 tan tan

A B

A B

( A ± B ≠ ( k + 1

2

For t = tan 1

2

A : sin A = 2

t

+ t

, cos A =

2 2

t

t

sin A + sin B = 2 sin

A + B

cos

A − B

sin A − sin B = 2 cos

A + B

sin

A − B

cos A + cos B = 2 cos

A + B

cos

A − B

cos A − cos B = –2 sin

A + B

sin

A − B

Vectors

The resolved part of a in the direction of b is

a.b

b

The point dividing AB in the ratio λ : μ is

μ λ λ μ

a b

Vector product: a × b = | a || b | sin θ

1 1 2 3 3 2 2 2 3 1 1 3 3 3 1 2 2 1

a b a b a b

a b a b a b

a b a b a b

i

n j

k

If A is the point with position vector a = a 1 i + a 2 j + a 3 k and the direction vector b is given by

b = b 1 i + b 2 j + b 3 k , then the straight line through A with direction vector b has cartesian equation

1 2 3 1 2 3

x a y a z a

b b b

The plane through A with normal vector n = n 1 i + n 2 j + n 3 k has cartesian equation n 1 x + n 2 y + n 3 z + d = 0

where d = − a.n

The plane through non-collinear points A , B and C has vector equation

r = a + λ ( b − a ) + μ ( c − a ) = (1 − λ − μ ) a + λ b + μ c

The plane through the point with position vector a and parallel to b and c has equation r = a + s b + t c

The perpendicular distance of ( α , β , γ ) from n 1 x + n 2 y + n 3 z + d = 0 is 1 2 3

2 2 2 1 2 3

n n n d

n n n

Matrix transformations

Anticlockwise rotation through θ about O :

cos sin

sin cos

θ θ θ θ

Reflection in the line y = (tan θ ) x :

cos 2 sin 2

sin 2 cos 2

θ θ θ θ

Differentiation

f( x ) f′( x )

tan kx k sec^2 kx

sin−1^ x

2

1 − x

cos−1^ x

2

1 x

tan−1^ x 2

1 + x

sec x sec x tan x

cot x − cosec^2 x

cosec x − cosec x cot x

sinh x cosh x

cosh x sinh x

tanh x sech^2 x

sinh−1^ x

2

1 + x

cosh–1^ x

2

x − 1

tanh−1^ x 2

1 − x

Integration (+ constant; a > 0 where relevant)

f( x ) (^) ∫ f( x ) d x

sec^2 kx

k

tan kx

tan x ln|sec x |

cot x ln|sin x |

cosec x −ln|cosec x + cot x | = ln|tan( 12 x )|

sec x ln|sec x + tan x | = ln|tan( 12 x + 14 π )|

sinh x cosh x

cosh x sinh x

tanh x ln cosh x

2 2

a − x

sin–^

x

a

(| x | < a )

2 2

a + x

a

tan–^

x

a

2 2

x − a

cosh–^

x

a

or ln{ x + x^2^ − a^2 } ( x > a )

2 2

a + x

sinh–^

x

a

or ln{ x + x^2^ + a^2 }

2 2

a − x

ln

a x

a a x a

tanh–^

x

a

(| x | < a )

2 2

x − a

ln

x a

a x a

d d

d d

d d

v u

u x uv v x

x x

∫ =^ −∫

MECHANICS

Motion in a circle

Transverse velocity: v = r θ Transverse acceleration: v  = r θ

Radial acceleration:

2

r^2 v

r

− θ = −

PROBABILITY

Probability

P( A ∪ B ) = P( A ) + P( B ) − P( A ∩ B )

P( A ∩ B ) = P( A ) P( B | A )

P( A | B ) =

P( ) P( )

P( ) P( ) P( ) P( )

B A A

B A A + B A ′^ A ′

Bayes’ Theorem: P( A j | B ) =

P( ) P( )

P( ) P( )

j j i i

A B A

Σ A B A

Discrete distributions

For a discrete random variable X taking values x i with probabilities pi

Expectation (mean): E( X ) = μ = Σ x i pi

Variance: Var( X ) = σ^2 = Σ( xi − μ ) 2 pi = Σ x i^2 pi − μ^2

For a function g( X ) : E(g( X )) = Σ g( xi ) pi

The probability generating function (P.G.F.) of X is G X ( t ) = E( t X ),

and E( X ) = G ′ X^ (1), Var( X ) = G ″ X^ (1) + G ′ X^ (1) −{G ′ X (1)}^2

For Z = X + Y , where X and Y are independent: G Z ( t ) = G X ( t ) G Y ( t )

The moment generating function (M.G.F.) of X is M X ( t ) = E(e tX ),

and E( X ) = M ′ X^ (0), E( X n ) = M ( X^ n )(0), Var( X ) = M ″ X^ (0) − { M ′ X^ (0)} 2

For Z = X + Y , where X and Y are independent: M Z ( t ) = M X ( t ) M Y ( t )

Standard discrete distributions

Distribution of X P( X = x ) Mean Variance P.G.F. M.G.F.

Binomial B( n , p ) (1^ )

n p x pn x

x

np np (1 – p ) (1 – p + pt ) n^ (1 – p + p e t ) n

Poisson Po( λ) (^) e

x

x

− λ λ λ λ e^ λ( t^ – 1)^ (e 1)

e

λ t −

Geometric Geo( p ) on 1, 2, … p (1 – p ) x^ – 1^

p^2

1 p

p

pt

− − p t

e

1 (1 )e

t t

p

− − p

Continuous distributions

For a continuous random variable X having probability density function (P.D.F.) f

Expectation (mean): E( X ) = μ = (^) ∫ x f ( ) d x x Variance: Var( X ) = σ^2 = (^) ∫ ( x − μ) f ( ) d^2 x x = (^) ∫ x^2 f ( ) d x x −μ^2 For a function g( X ) : E(g( X )) = (^) ∫g( ) f ( ) d x x x

Cumulative distribution function: F( x ) = P( X ⩽ x ) = f ( ) d

x

t t

∫ −∞

The moment generating function (M.G.F.) of X is M X ( t ) = E(e tX ),

and E( X ) = M ′ X^ (0), E( X n ) = M ( X^ n )(0), Var( X ) = M ″ X^ (0) − { M ′ X^ (0)} 2

For Z = X + Y , where X and Y are independent: M Z ( t ) = M X ( t ) M Y ( t )

Standard continuous distributions

Distribution of X P.D.F Mean Variance M.G.F.

Uniform (Rectangular) on [ a , b ]

b − a

1

2 (^ a^ +^ b )

1 2

12 (^ b^ −^ a )

e e

bt at

b a t

Exponential λ e–^ λ x^

λ 2

λ t

λ λ − Normal N( μ , σ 2 ) 1 2

e

x μ σ σ π − ^ −    μ σ 2 (^1) 2 2

e μ t^^ +^2 σ t

Expectation algebra

For independent random variables X and Y

E( XY ) = E( X ) E( Y ), Var ( aX ± bY ) = a^2 Var( X ) + b^2 Var ( Y )

CUMULATIVE BINOMIAL PROBABILITIES

0

P( ) (1 )

x n n r r r r

X x C p − p

=

CUMULATIVE BINOMIAL PROBABI

p (^123456789101112131415161718) p

p

CUMULATIVE POISSON PROBABILITIES

0

P( ) e

x (^) r r

X x

r

− λ λ

THE NORMAL DISTRIBUTION FUNCTION

If Z has a normal distribution with mean 0 and

variance 1, then, for each value of z , the table gives

the value of Φ( z ), where

Φ( z ) = P( Z ⩽ z ).

For negative values of z , use Φ(– z ) = 1 – Φ( z ).

z 0 1 2 3 4 5 6 7 8 9
ADD

Critical values for the normal distribution

If Z has a normal distribution with mean 0 and

variance 1, then, for each value of p , the table

gives the value of z such that

P( Z ⩽ z ) = p.

p 0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.
z 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.

CRITICAL VALUES FOR THE t -DISTRIBUTION

If T has a t -distribution with ν degrees of freedom, then, for each pair of values of p and ν, the table gives the value

of t such that:

  • n = ø = ∑ − - p 0.05 0.1 0.15 1/6 0.2 0.25 0.3 1/3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 2/3 0.7 0.75 0.8 5/6 0.85 0.9 0.
    • x = 0 0.7738 0.5905 0.4437 0.4019 0.3277 0.2373 0.1681 0.1317 0.1160 0.0778 0.0503 0.0313 0.0185 0.0102 0.0053 0.0041 0.0024 0.0010 0.0003 0.0001 0.0001 0.0000 0.
      • 1 0.9774 0.9185 0.8352 0.8038 0.7373 0.6328 0.5282 0.4609 0.4284 0.3370 0.2562 0.1875 0.1312 0.0870 0.0540 0.0453 0.0308 0.0156 0.0067 0.0033 0.0022 0.0005 0.
      • 2 0.9988 0.9914 0.9734 0.9645 0.9421 0.8965 0.8369 0.7901 0.7648 0.6826 0.5931 0.5000 0.4069 0.3174 0.2352 0.2099 0.1631 0.1035 0.0579 0.0355 0.0266 0.0086 0.
      • 3 1.0000 0.9995 0.9978 0.9967 0.9933 0.9844 0.9692 0.9547 0.9460 0.9130 0.8688 0.8125 0.7438 0.6630 0.5716 0.5391 0.4718 0.3672 0.2627 0.1962 0.1648 0.0815 0.
      • 4 1.0000 1.0000 0.9999 0.9999 0.9997 0.9990 0.9976 0.9959 0.9947 0.9898 0.9815 0.9688 0.9497 0.9222 0.8840 0.8683 0.8319 0.7627 0.6723 0.5981 0.5563 0.4095 0.
      • 5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • n = - p 0.05 0.1 0.15 1/6 0.2 0.25 0.3 1/3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 2/3 0.7 0.75 0.8 5/6 0.85 0.9 0.
    • x = 0 0.7351 0.5314 0.3771 0.3349 0.2621 0.1780 0.1176 0.0878 0.0754 0.0467 0.0277 0.0156 0.0083 0.0041 0.0018 0.0014 0.0007 0.0002 0.0001 0.0000 0.0000 0.0000 0.
      • 1 0.9672 0.8857 0.7765 0.7368 0.6554 0.5339 0.4202 0.3512 0.3191 0.2333 0.1636 0.1094 0.0692 0.0410 0.0223 0.0178 0.0109 0.0046 0.0016 0.0007 0.0004 0.0001 0.
      • 2 0.9978 0.9842 0.9527 0.9377 0.9011 0.8306 0.7443 0.6804 0.6471 0.5443 0.4415 0.3438 0.2553 0.1792 0.1174 0.1001 0.0705 0.0376 0.0170 0.0087 0.0059 0.0013 0.
      • 3 0.9999 0.9987 0.9941 0.9913 0.9830 0.9624 0.9295 0.8999 0.8826 0.8208 0.7447 0.6563 0.5585 0.4557 0.3529 0.3196 0.2557 0.1694 0.0989 0.0623 0.0473 0.0159 0.
      • 4 1.0000 0.9999 0.9996 0.9993 0.9984 0.9954 0.9891 0.9822 0.9777 0.9590 0.9308 0.8906 0.8364 0.7667 0.6809 0.6488 0.5798 0.4661 0.3446 0.2632 0.2235 0.1143 0.
      • 5 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9993 0.9986 0.9982 0.9959 0.9917 0.9844 0.9723 0.9533 0.9246 0.9122 0.8824 0.8220 0.7379 0.6651 0.6229 0.4686 0.
      • 6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • n = - p 0.05 0.1 0.15 1/6 0.2 0.25 0.3 1/3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 2/3 0.7 0.75 0.8 5/6 0.85 0.9 0.
    • x = 0 0.6983 0.4783 0.3206 0.2791 0.2097 0.1335 0.0824 0.0585 0.0490 0.0280 0.0152 0.0078 0.0037 0.0016 0.0006 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.
      • 1 0.9556 0.8503 0.7166 0.6698 0.5767 0.4449 0.3294 0.2634 0.2338 0.1586 0.1024 0.0625 0.0357 0.0188 0.0090 0.0069 0.0038 0.0013 0.0004 0.0001 0.0001 0.0000 0.
      • 2 0.9962 0.9743 0.9262 0.9042 0.8520 0.7564 0.6471 0.5706 0.5323 0.4199 0.3164 0.2266 0.1529 0.0963 0.0556 0.0453 0.0288 0.0129 0.0047 0.0020 0.0012 0.0002 0.
      • 3 0.9998 0.9973 0.9879 0.9824 0.9667 0.9294 0.8740 0.8267 0.8002 0.7102 0.6083 0.5000 0.3917 0.2898 0.1998 0.1733 0.1260 0.0706 0.0333 0.0176 0.0121 0.0027 0.
      • 4 1.0000 0.9998 0.9988 0.9980 0.9953 0.9871 0.9712 0.9547 0.9444 0.9037 0.8471 0.7734 0.6836 0.5801 0.4677 0.4294 0.3529 0.2436 0.1480 0.0958 0.0738 0.0257 0.
      • 5 1.0000 1.0000 0.9999 0.9999 0.9996 0.9987 0.9962 0.9931 0.9910 0.9812 0.9643 0.9375 0.8976 0.8414 0.7662 0.7366 0.6706 0.5551 0.4233 0.3302 0.2834 0.1497 0.
      • 6 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0.9994 0.9984 0.9963 0.9922 0.9848 0.9720 0.9510 0.9415 0.9176 0.8665 0.7903 0.7209 0.6794 0.5217 0.
      • 7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • n = - p 0.05 0.1 0.15 1/6 0.2 0.25 0.3 1/3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 2/3 0.7 0.75 0.8 5/6 0.85 0.9 0.
    • x = 0 0.6634 0.4305 0.2725 0.2326 0.1678 0.1001 0.0576 0.0390 0.0319 0.0168 0.0084 0.0039 0.0017 0.0007 0.0002 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.
      • 1 0.9428 0.8131 0.6572 0.6047 0.5033 0.3671 0.2553 0.1951 0.1691 0.1064 0.0632 0.0352 0.0181 0.0085 0.0036 0.0026 0.0013 0.0004 0.0001 0.0000 0.0000 0.0000 0.
      • 2 0.9942 0.9619 0.8948 0.8652 0.7969 0.6785 0.5518 0.4682 0.4278 0.3154 0.2201 0.1445 0.0885 0.0498 0.0253 0.0197 0.0113 0.0042 0.0012 0.0004 0.0002 0.0000 0.
      • 3 0.9996 0.9950 0.9786 0.9693 0.9437 0.8862 0.8059 0.7414 0.7064 0.5941 0.4770 0.3633 0.2604 0.1737 0.1061 0.0879 0.0580 0.0273 0.0104 0.0046 0.0029 0.0004 0.
      • 4 1.0000 0.9996 0.9971 0.9954 0.9896 0.9727 0.9420 0.9121 0.8939 0.8263 0.7396 0.6367 0.5230 0.4059 0.2936 0.2586 0.1941 0.1138 0.0563 0.0307 0.0214 0.0050 0.
      • 5 1.0000 1.0000 0.9998 0.9996 0.9988 0.9958 0.9887 0.9803 0.9747 0.9502 0.9115 0.8555 0.7799 0.6846 0.5722 0.5318 0.4482 0.3215 0.2031 0.1348 0.1052 0.0381 0.
      • 6 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9974 0.9964 0.9915 0.9819 0.9648 0.9368 0.8936 0.8309 0.8049 0.7447 0.6329 0.4967 0.3953 0.3428 0.1869 0.
      • 7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9998 0.9993 0.9983 0.9961 0.9916 0.9832 0.9681 0.9610 0.9424 0.8999 0.8322 0.7674 0.7275 0.5695 0.
      • 8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0084 0.0712 0.3698 1.0000 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0010 0.0115 0.0861 0.4013 1.0000 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0022 0.0196 0.1184 0.4596 1. LITIES
      • 0.0000 0.0000 0.0000 0.0001 0.0009 0.0083 0.0530 0.2252 0.6126 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0001 0.0016 0.0128 0.0702 0.2639 0.6513 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0043 0.0256 0.1109 0.3410 0.7176 1.
    • 0.85 0.0000 0.0000 0.0000 0.0006 0.0056 0.0339 0.1409 0.4005 0.7684 1.0000 0.85 0.0000 0.0000 0.0000 0.0001 0.0014 0.0099 0.0500 0.1798 0.4557 0.8031 1.0000 0.85 0.0000 0.0000 0.0000 0.0000 0.0001 0.0007 0.0046 0.0239 0.0922 0.2642 0.5565 0.8578 1.
    • 5/
      • 0.0000 0.0000 0.0001 0.0011 0.0090 0.0480 0.1783 0.4573 0.8062 1. - 5/ - 0.0000 0.0000 0.0000 0.0003 0.0024 0.0155 0.0697 0.2248 0.5155 0.8385 1. - 5/ - 0.0000 0.0000 0.0000 0.0000 0.0002 0.0013 0.0079 0.0364 0.1252 0.3226 0.6187 0.8878 1.
      • 0.0000 0.0000 0.0003 0.0031 0.0196 0.0856 0.2618 0.5638 0.8658 1. - 0. - 0.0000 0.0000 0.0001 0.0009 0.0064 0.0328 0.1209 0.3222 0.6242 0.8926 1. - 0. - 0.0000 0.0000 0.0000 0.0001 0.0006 0.0039 0.0194 0.0726 0.2054 0.4417 0.7251 0.9313 1.
    • 0.75 0.0000 0.0001 0.0013 0.0100 0.0489 0.1657 0.3993 0.6997 0.9249 1.0000 0.75 0.0000 0.0000 0.0004 0.0035 0.0197 0.0781 0.2241 0.4744 0.7560 0.9437 1.0000 0.75 0.0000 0.0000 0.0000 0.0004 0.0028 0.0143 0.0544 0.1576 0.3512 0.6093 0.8416 0.9683 1.
      • 0.0000 0.0004 0.0043 0.0253 0.0988 0.2703 0.5372 0.8040 0.9596 1. - 0. - 0.0000 0.0001 0.0016 0.0106 0.0473 0.1503 0.3504 0.6172 0.8507 0.9718 1. - 0. - 0.0000 0.0000 0.0002 0.0017 0.0095 0.0386 0.1178 0.2763 0.5075 0.7472 0.9150 0.9862 1.
    • 2/
      • 0.0001 0.0010 0.0083 0.0424 0.1448 0.3497 0.6228 0.8569 0.9740 1. - 2/ - 0.0000 0.0004 0.0034 0.0197 0.0766 0.2131 0.4407 0.7009 0.8960 0.9827 1. - 2/ - 0.0000 0.0000 0.0005 0.0039 0.0188 0.0664 0.1777 0.3685 0.6069 0.8189 0.9460 0.9923 1.
    • 0.65 0.0001 0.0014 0.0112 0.0536 0.1717 0.3911 0.6627 0.8789 0.9793 1.0000 0.65 0.0000 0.0005 0.0048 0.0260 0.0949 0.2485 0.4862 0.7384 0.9140 0.9865 1.0000 0.65 0.0000 0.0001 0.0008 0.0056 0.0255 0.0846 0.2127 0.4167 0.6533 0.8487 0.9576 0.9943 1.
      • 0.0003 0.0038 0.0250 0.0994 0.2666 0.5174 0.7682 0.9295 0.9899 1. - 0. - 0.0001 0.0017 0.0123 0.0548 0.1662 0.3669 0.6177 0.8327 0.9536 0.9940 1. - 0. - 0.0000 0.0003 0.0028 0.0153 0.0573 0.1582 0.3348 0.5618 0.7747 0.9166 0.9804 0.9978 1.
    • 0.55 0.0008 0.0091 0.0498 0.1658 0.3786 0.6386 0.8505 0.9615 0.9954 1.0000 0.55 0.0003 0.0045 0.0274 0.1020 0.2616 0.4956 0.7340 0.9004 0.9767 0.9975 1.0000 0.55 0.0001 0.0011 0.0079 0.0356 0.1117 0.2607 0.4731 0.6956 0.8655 0.9579 0.9917 0.9992 1.
      • 0.0020 0.0195 0.0898 0.2539 0.5000 0.7461 0.9102 0.9805 0.9980 1. - 0. - 0.0010 0.0107 0.0547 0.1719 0.3770 0.6230 0.8281 0.9453 0.9893 0.9990 1. - 0. - 0.0002 0.0032 0.0193 0.0730 0.1938 0.3872 0.6128 0.8062 0.9270 0.9807 0.9968 0.9998 1.
    • 0.45 0.0046 0.0385 0.1495 0.3614 0.6214 0.8342 0.9502 0.9909 0.9992 1.0000 0.45 0.0025 0.0233 0.0996 0.2660 0.5044 0.7384 0.8980 0.9726 0.9955 0.9997 1.0000 0.45 0.0008 0.0083 0.0421 0.1345 0.3044 0.5269 0.7393 0.8883 0.9644 0.9921 0.9989 0.9999 1.
      • 0.0101 0.0705 0.2318 0.4826 0.7334 0.9006 0.9750 0.9962 0.9997 1. - 0. - 0.0060 0.0464 0.1673 0.3823 0.6331 0.8338 0.9452 0.9877 0.9983 0.9999 1. - 0. - 0.0022 0.0196 0.0834 0.2253 0.4382 0.6652 0.8418 0.9427 0.9847 0.9972 0.9997 1.0000 1.
    • 0.35 0.0207 0.1211 0.3373 0.6089 0.8283 0.9464 0.9888 0.9986 0.9999 1.0000 0.35 0.0135 0.0860 0.2616 0.5138 0.7515 0.9051 0.9740 0.9952 0.9995 1.0000 1.0000 0.35 0.0057 0.0424 0.1513 0.3467 0.5833 0.7873 0.9154 0.9745 0.9944 0.9992 0.9999 1.0000 1.
    • 1/
      • 0.0260 0.1431 0.3772 0.6503 0.8552 0.9576 0.9917 0.9990 0.9999 1. - 1/ - 0.0173 0.1040 0.2991 0.5593 0.7869 0.9234 0.9803 0.9966 0.9996 1.0000 1. - 1/ - 0.0077 0.0540 0.1811 0.3931 0.6315 0.8223 0.9336 0.9812 0.9961 0.9995 1.0000 1.0000 1.
      • 0.0404 0.1960 0.4628 0.7297 0.9012 0.9747 0.9957 0.9996 1.0000 1. - 0. - 0.0282 0.1493 0.3828 0.6496 0.8497 0.9527 0.9894 0.9984 0.9999 1.0000 1. - 0. - 0.0138 0.0850 0.2528 0.4925 0.7237 0.8822 0.9614 0.9905 0.9983 0.9998 1.0000 1.0000 1.
    • 0.25 0.0751 0.3003 0.6007 0.8343 0.9511 0.9900 0.9987 0.9999 1.0000 1.0000 0.25 0.0563 0.2440 0.5256 0.7759 0.9219 0.9803 0.9965 0.9996 1.0000 1.0000 1.0000 0.25 0.0317 0.1584 0.3907 0.6488 0.8424 0.9456 0.9857 0.9972 0.9996 1.0000 1.0000 1.0000 1.
      • 0.1342 0.4362 0.7382 0.9144 0.9804 0.9969 0.9997 1.0000 1.0000 1. - 0. - 0.1074 0.3758 0.6778 0.8791 0.9672 0.9936 0.9991 0.9999 1.0000 1.0000 1. - 0. - 0.0687 0.2749 0.5583 0.7946 0.9274 0.9806 0.9961 0.9994 0.9999 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.1938 0.5427 0.8217 0.9520 0.9910 0.9989 0.9999 1.0000 1.0000 1. - 1/ - 0.1615 0.4845 0.7752 0.9303 0.9845 0.9976 0.9997 1.0000 1.0000 1.0000 1. - 1/ - 0.1122 0.3813 0.6774 0.8748 0.9636 0.9921 0.9987 0.9998 1.0000 1.0000 1.0000 1.0000 1.
    • 0.15 0.2316 0.5995 0.8591 0.9661 0.9944 0.9994 1.0000 1.0000 1.0000 1.0000 0.15 0.1969 0.5443 0.8202 0.9500 0.9901 0.9986 0.9999 1.0000 1.0000 1.0000 1.0000 0.15 0.1422 0.4435 0.7358 0.9078 0.9761 0.9954 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 1.
      • 0.3874 0.7748 0.9470 0.9917 0.9991 0.9999 1.0000 1.0000 1.0000 1. - 0. - 0.3487 0.7361 0.9298 0.9872 0.9984 0.9999 1.0000 1.0000 1.0000 1.0000 1. - 0. - 0.2824 0.6590 0.8891 0.9744 0.9957 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.05 0.6302 0.9288 0.9916 0.9994 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.05 0.5987 0.9139 0.9885 0.9990 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.05 0.5404 0.8816 0.9804 0.9978 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • = n - x = p - = n - x = p - = n - x = p
    • 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0042 0.0301 0.1530 0.5123 1.0000 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0009 0.0070 0.0429 0.1892 0.5599 1. CUMULATIVE BINOMIAL PROBABILITIES
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0015 0.0092 0.0441 0.1584 0.4154 0.7712 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0033 0.0170 0.0684 0.2108 0.4853 0.8147 1.
    • 0.85 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0022 0.0115 0.0467 0.1465 0.3521 0.6433 0.8972 1.0000 0.85 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0011 0.0056 0.0235 0.0791 0.2101 0.4386 0.7161 0.9257 1.
    • 5/
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0007 0.0041 0.0191 0.0690 0.1937 0.4205 0.7040 0.9221 1. - 5/ - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0021 0.0101 0.0378 0.1134 0.2709 0.5132 0.7728 0.9459 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0024 0.0116 0.0439 0.1298 0.3018 0.5519 0.8021 0.9560 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0015 0.0070 0.0267 0.0817 0.2018 0.4019 0.6482 0.8593 0.9719 1.
    • 0.75 0.0000 0.0000 0.0000 0.0000 0.0003 0.0022 0.0103 0.0383 0.1117 0.2585 0.4787 0.7189 0.8990 0.9822 1.0000 0.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0016 0.0075 0.0271 0.0796 0.1897 0.3698 0.5950 0.8029 0.9365 0.9900 1.
      • 0.0000 0.0000 0.0000 0.0002 0.0017 0.0083 0.0315 0.0933 0.2195 0.4158 0.6448 0.8392 0.9525 0.9932 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0003 0.0016 0.0071 0.0257 0.0744 0.1753 0.3402 0.5501 0.7541 0.9006 0.9739 0.9967 1.
    • 2/
      • 0.0000 0.0000 0.0001 0.0007 0.0040 0.0174 0.0576 0.1495 0.3102 0.5245 0.7388 0.8947 0.9726 0.9966 1. - 2/ - 0.0000 0.0000 0.0000 0.0001 0.0008 0.0040 0.0159 0.0500 0.1265 0.2626 0.4531 0.6609 0.8341 0.9406 0.9863 0.9985 1.
    • 0.65 0.0000 0.0000 0.0001 0.0011 0.0060 0.0243 0.0753 0.1836 0.3595 0.5773 0.7795 0.9161 0.9795 0.9976 1.0000 0.65 0.0000 0.0000 0.0000 0.0002 0.0013 0.0062 0.0229 0.0671 0.1594 0.3119 0.5100 0.7108 0.8661 0.9549 0.9902 0.9990 1.
      • 0.0000 0.0001 0.0006 0.0039 0.0175 0.0583 0.1501 0.3075 0.5141 0.7207 0.8757 0.9602 0.9919 0.9992 1. - 0. - 0.0000 0.0000 0.0001 0.0009 0.0049 0.0191 0.0583 0.1423 0.2839 0.4728 0.6712 0.8334 0.9349 0.9817 0.9967 0.9997 1.
    • 0.55 0.0000 0.0003 0.0022 0.0114 0.0426 0.1189 0.2586 0.4539 0.6627 0.8328 0.9368 0.9830 0.9971 0.9998 1.0000 0.55 0.0000 0.0001 0.0006 0.0035 0.0149 0.0486 0.1241 0.2559 0.4371 0.6340 0.8024 0.9147 0.9719 0.9934 0.9990 0.9999 1.
      • 0.0001 0.0009 0.0065 0.0287 0.0898 0.2120 0.3953 0.6047 0.7880 0.9102 0.9713 0.9935 0.9991 0.9999 1. - 0. - 0.0000 0.0003 0.0021 0.0106 0.0384 0.1051 0.2272 0.4018 0.5982 0.7728 0.8949 0.9616 0.9894 0.9979 0.9997 1.0000 1.
    • 0.45 0.0002 0.0029 0.0170 0.0632 0.1672 0.3373 0.5461 0.7414 0.8811 0.9574 0.9886 0.9978 0.9997 1.0000 1.0000 0.45 0.0001 0.0010 0.0066 0.0281 0.0853 0.1976 0.3660 0.5629 0.7441 0.8759 0.9514 0.9851 0.9965 0.9994 0.9999 1.0000 1.
      • 0.0008 0.0081 0.0398 0.1243 0.2793 0.4859 0.6925 0.8499 0.9417 0.9825 0.9961 0.9994 0.9999 1.0000 1. - 0. - 0.0003 0.0033 0.0183 0.0651 0.1666 0.3288 0.5272 0.7161 0.8577 0.9417 0.9809 0.9951 0.9991 0.9999 1.0000 1.0000 1.
    • 0.35 0.0024 0.0205 0.0839 0.2205 0.4227 0.6405 0.8164 0.9247 0.9757 0.9940 0.9989 0.9999 1.0000 1.0000 1.0000 0.35 0.0010 0.0098 0.0451 0.1339 0.2892 0.4900 0.6881 0.8406 0.9329 0.9771 0.9938 0.9987 0.9998 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0034 0.0274 0.1053 0.2612 0.4755 0.6898 0.8505 0.9424 0.9826 0.9960 0.9993 0.9999 1.0000 1.0000 1. - 1/ - 0.0015 0.0137 0.0594 0.1659 0.3391 0.5469 0.7374 0.8735 0.9500 0.9841 0.9960 0.9992 0.9999 1.0000 1.0000 1.0000 1.
      • 0.0068 0.0475 0.1608 0.3552 0.5842 0.7805 0.9067 0.9685 0.9917 0.9983 0.9998 1.0000 1.0000 1.0000 1. - 0. - 0.0033 0.0261 0.0994 0.2459 0.4499 0.6598 0.8247 0.9256 0.9743 0.9929 0.9984 0.9997 1.0000 1.0000 1.0000 1.0000 1.
    • 0.25 0.0178 0.1010 0.2811 0.5213 0.7415 0.8883 0.9617 0.9897 0.9978 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 0.25 0.0100 0.0635 0.1971 0.4050 0.6302 0.8103 0.9204 0.9729 0.9925 0.9984 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0440 0.1979 0.4481 0.6982 0.8702 0.9561 0.9884 0.9976 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1. - 0. - 0.0281 0.1407 0.3518 0.5981 0.7982 0.9183 0.9733 0.9930 0.9985 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0779 0.2960 0.5795 0.8063 0.9310 0.9809 0.9959 0.9993 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1. - 1/ - 0.0541 0.2272 0.4868 0.7291 0.8866 0.9622 0.9899 0.9979 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.15 0.1028 0.3567 0.6479 0.8535 0.9533 0.9885 0.9978 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.15 0.0743 0.2839 0.5614 0.7899 0.9209 0.9765 0.9944 0.9989 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.2288 0.5846 0.8416 0.9559 0.9908 0.9985 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1. - 0. - 0.1853 0.5147 0.7892 0.9316 0.9830 0.9967 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.05 0.4877 0.8470 0.9699 0.9958 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.05 0.4401 0.8108 0.9571 0.9930 0.9991 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • = n - = x - = n - = x
    • 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0015 0.0109 0.0581 0.2265 0.6028 1.0000 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0026 0.0159 0.0755 0.2642 0.6415 1. CUMULATIVE BINOMIAL PROBABILITIES
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0012 0.0064 0.0282 0.0982 0.2662 0.5497 0.8499 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0024 0.0113 0.0432 0.1330 0.3231 0.6083 0.8784 1.
    • 0.85 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0027 0.0118 0.0419 0.1206 0.2798 0.5203 0.7759 0.9464 1.0000 0.85 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0013 0.0059 0.0219 0.0673 0.1702 0.3523 0.5951 0.8244 0.9612 1.
    • 5/
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0011 0.0053 0.0206 0.0653 0.1682 0.3521 0.5973 0.8272 0.9624 1. - 5/ - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0028 0.0113 0.0371 0.1018 0.2313 0.4335 0.6713 0.8696 0.9739 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0009 0.0043 0.0163 0.0513 0.1329 0.2836 0.4990 0.7287 0.9009 0.9820 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0026 0.0100 0.0321 0.0867 0.1958 0.3704 0.5886 0.7939 0.9308 0.9885 1.
    • 0.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0012 0.0054 0.0193 0.0569 0.1390 0.2825 0.4813 0.6943 0.8647 0.9605 0.9944 1.0000 0.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0009 0.0039 0.0139 0.0409 0.1018 0.2142 0.3828 0.5852 0.7748 0.9087 0.9757 0.9968 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0014 0.0061 0.0210 0.0596 0.1407 0.2783 0.4656 0.6673 0.8354 0.9400 0.9858 0.9984 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0013 0.0051 0.0171 0.0480 0.1133 0.2277 0.3920 0.5836 0.7625 0.8929 0.9645 0.9924 0.9992 1.
    • 2/
      • 0.0000 0.0000 0.0000 0.0000 0.0001 0.0009 0.0039 0.0144 0.0433 0.1076 0.2233 0.3915 0.5878 0.7689 0.8983 0.9674 0.9932 0.9993 1. - 2/ - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0009 0.0037 0.0130 0.0376 0.0919 0.1905 0.3385 0.5207 0.7028 0.8485 0.9396 0.9824 0.9967 0.9997 1.
    • 0.65 0.0000 0.0000 0.0000 0.0000 0.0003 0.0014 0.0062 0.0212 0.0597 0.1391 0.2717 0.4509 0.6450 0.8114 0.9217 0.9764 0.9954 0.9996 1.0000 0.65 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0015 0.0060 0.0196 0.0532 0.1218 0.2376 0.3990 0.5834 0.7546 0.8818 0.9556 0.9879 0.9979 0.9998 1.
      • 0.0000 0.0000 0.0000 0.0002 0.0013 0.0058 0.0203 0.0576 0.1347 0.2632 0.4366 0.6257 0.7912 0.9058 0.9672 0.9918 0.9987 0.9999 1. - 0. - 0.0000 0.0000 0.0000 0.0000 0.0003 0.0016 0.0065 0.0210 0.0565 0.1275 0.2447 0.4044 0.5841 0.7500 0.8744 0.9490 0.9840 0.9964 0.9995 1.0000 1.
    • 0.55 0.0000 0.0000 0.0001 0.0010 0.0049 0.0183 0.0537 0.1280 0.2527 0.4222 0.6085 0.7742 0.8923 0.9589 0.9880 0.9975 0.9997 1.0000 1.0000 0.55 0.0000 0.0000 0.0000 0.0003 0.0015 0.0064 0.0214 0.0580 0.1308 0.2493 0.4086 0.5857 0.7480 0.8701 0.9447 0.9811 0.9951 0.9991 0.9999 1.0000 1.
      • 0.0000 0.0001 0.0007 0.0038 0.0154 0.0481 0.1189 0.2403 0.4073 0.5927 0.7597 0.8811 0.9519 0.9846 0.9962 0.9993 0.9999 1.0000 1. - 0. - 0.0000 0.0000 0.0002 0.0013 0.0059 0.0207 0.0577 0.1316 0.2517 0.4119 0.5881 0.7483 0.8684 0.9423 0.9793 0.9941 0.9987 0.9998 1.0000 1.0000 1.
    • 0.45 0.0000 0.0003 0.0025 0.0120 0.0411 0.1077 0.2258 0.3915 0.5778 0.7473 0.8720 0.9463 0.9817 0.9951 0.9990 0.9999 1.0000 1.0000 1.0000 0.45 0.0000 0.0001 0.0009 0.0049 0.0189 0.0553 0.1299 0.2520 0.4143 0.5914 0.7507 0.8692 0.9420 0.9786 0.9936 0.9985 0.9997 1.0000 1.0000 1.0000 1.
      • 0.0001 0.0013 0.0082 0.0328 0.0942 0.2088 0.3743 0.5634 0.7368 0.8653 0.9424 0.9797 0.9942 0.9987 0.9998 1.0000 1.0000 1.0000 1. - 0. - 0.0000 0.0005 0.0036 0.0160 0.0510 0.1256 0.2500 0.4159 0.5956 0.7553 0.8725 0.9435 0.9790 0.9935 0.9984 0.9997 1.0000 1.0000 1.0000 1.0000 1.
    • 0.35 0.0004 0.0046 0.0236 0.0783 0.1886 0.3550 0.5491 0.7283 0.8609 0.9403 0.9788 0.9938 0.9986 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 0.35 0.0002 0.0021 0.0121 0.0444 0.1182 0.2454 0.4166 0.6010 0.7624 0.8782 0.9468 0.9804 0.9940 0.9985 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0007 0.0068 0.0326 0.1017 0.2311 0.4122 0.6085 0.7767 0.8924 0.9567 0.9856 0.9961 0.9991 0.9999 1.0000 1.0000 1.0000 1.0000 1. - 1/ - 0.0003 0.0033 0.0176 0.0604 0.1515 0.2972 0.4793 0.6615 0.8095 0.9081 0.9624 0.9870 0.9963 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0016 0.0142 0.0600 0.1646 0.3327 0.5344 0.7217 0.8593 0.9404 0.9790 0.9939 0.9986 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1. - 0. - 0.0008 0.0076 0.0355 0.1071 0.2375 0.4164 0.6080 0.7723 0.8867 0.9520 0.9829 0.9949 0.9987 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.25 0.0056 0.0395 0.1353 0.3057 0.5187 0.7175 0.8610 0.9431 0.9807 0.9946 0.9988 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.25 0.0032 0.0243 0.0913 0.2252 0.4148 0.6172 0.7858 0.8982 0.9591 0.9861 0.9961 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0180 0.0991 0.2713 0.5010 0.7164 0.8671 0.9487 0.9837 0.9957 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1. - 0. - 0.0115 0.0692 0.2061 0.4114 0.6296 0.8042 0.9133 0.9679 0.9900 0.9974 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0376 0.1728 0.4027 0.6479 0.8318 0.9347 0.9794 0.9947 0.9989 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1. - 1/ - 0.0261 0.1304 0.3287 0.5665 0.7687 0.8982 0.9629 0.9887 0.9972 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.15 0.0536 0.2241 0.4797 0.7202 0.8794 0.9581 0.9882 0.9973 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.15 0.0388 0.1756 0.4049 0.6477 0.8298 0.9327 0.9781 0.9941 0.9987 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.1501 0.4503 0.7338 0.9018 0.9718 0.9936 0.9988 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1. - 0. - 0.1216 0.3917 0.6769 0.8670 0.9568 0.9887 0.9976 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.05 0.3972 0.7735 0.9419 0.9891 0.9985 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.05 0.3585 0.7358 0.9245 0.9841 0.9974 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • = n - = x - = n - = x
    • 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0012 0.0072 0.0341 0.1271 0.3576 0.7226 1. CUMULATIVE BINOMIAL PROBABILITIES
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0023 0.0095 0.0334 0.0980 0.2364 0.4629 0.7288 0.9282 1.
    • 0.85 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0021 0.0080 0.0255 0.0695 0.1615 0.3179 0.5289 0.7463 0.9069 0.9828 1.
    • 5/
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0012 0.0047 0.0157 0.0447 0.1092 0.2280 0.4063 0.6184 0.8113 0.9371 0.9895 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0015 0.0056 0.0173 0.0468 0.1091 0.2200 0.3833 0.5793 0.7660 0.9018 0.9726 0.9962 1.
    • 0.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0009 0.0034 0.0107 0.0297 0.0713 0.1494 0.2735 0.4389 0.6217 0.7863 0.9038 0.9679 0.9930 0.9992 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0018 0.0060 0.0175 0.0442 0.0978 0.1894 0.3231 0.4882 0.6593 0.8065 0.9095 0.9668 0.9910 0.9984 0.9999 1.
    • 2/
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0016 0.0056 0.0164 0.0415 0.0918 0.1780 0.3044 0.4624 0.6297 0.7785 0.8880 0.9538 0.9851 0.9965 0.9995 1.0000 1.
    • 0.65 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0008 0.0029 0.0093 0.0255 0.0604 0.1254 0.2288 0.3697 0.5332 0.6939 0.8266 0.9174 0.9680 0.9903 0.9979 0.9997 1.0000 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0012 0.0043 0.0132 0.0344 0.0778 0.1538 0.2677 0.4142 0.5754 0.7265 0.8464 0.9264 0.9706 0.9905 0.9976 0.9996 0.9999 1.0000 1.
    • 0.55 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0016 0.0058 0.0174 0.0440 0.0960 0.1827 0.3063 0.4574 0.6157 0.7576 0.8660 0.9361 0.9742 0.9914 0.9977 0.9995 0.9999 1.0000 1.0000 1.
      • 0.0000 0.0000 0.0000 0.0001 0.0005 0.0020 0.0073 0.0216 0.0539 0.1148 0.2122 0.3450 0.5000 0.6550 0.7878 0.8852 0.9461 0.9784 0.9927 0.9980 0.9995 0.9999 1.0000 1.0000 1.0000 1.
    • 0.45 0.0000 0.0000 0.0001 0.0005 0.0023 0.0086 0.0258 0.0639 0.1340 0.2424 0.3843 0.5426 0.6937 0.8173 0.9040 0.9560 0.9826 0.9942 0.9984 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0000 0.0001 0.0004 0.0024 0.0095 0.0294 0.0736 0.1536 0.2735 0.4246 0.5858 0.7323 0.8462 0.9222 0.9656 0.9868 0.9957 0.9988 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.35 0.0000 0.0003 0.0021 0.0097 0.0320 0.0826 0.1734 0.3061 0.4668 0.6303 0.7712 0.8746 0.9396 0.9745 0.9907 0.9971 0.9992 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0000 0.0005 0.0035 0.0149 0.0462 0.1120 0.2215 0.3703 0.5376 0.6956 0.8220 0.9082 0.9585 0.9836 0.9944 0.9984 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0001 0.0016 0.0090 0.0332 0.0905 0.1935 0.3407 0.5118 0.6769 0.8106 0.9022 0.9558 0.9825 0.9940 0.9982 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.25 0.0008 0.0070 0.0321 0.0962 0.2137 0.3783 0.5611 0.7265 0.8506 0.9287 0.9703 0.9893 0.9966 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0038 0.0274 0.0982 0.2340 0.4207 0.6167 0.7800 0.8909 0.9532 0.9827 0.9944 0.9985 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0105 0.0629 0.1887 0.3816 0.5937 0.7720 0.8908 0.9553 0.9843 0.9953 0.9988 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.15 0.0172 0.0931 0.2537 0.4711 0.6821 0.8385 0.9305 0.9745 0.9920 0.9979 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0718 0.2712 0.5371 0.7636 0.9020 0.9666 0.9905 0.9977 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.05 0.2774 0.6424 0.8729 0.9659 0.9928 0.9988 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • = n - = x
    • 0.95 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0033 0.0156 0.0608 0.1878 0.4465 0.7854 1. CUMULATIVE BINOMIAL PROBABILITIES
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0020 0.0078 0.0258 0.0732 0.1755 0.3526 0.5886 0.8163 0.9576 1.
    • 0.85 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0008 0.0029 0.0097 0.0278 0.0698 0.1526 0.2894 0.4755 0.6783 0.8486 0.9520 0.9924 1.
    • 5/
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0020 0.0067 0.0197 0.0506 0.1137 0.2235 0.3836 0.5757 0.7604 0.8972 0.9705 0.9958 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0009 0.0031 0.0095 0.0256 0.0611 0.1287 0.2392 0.3930 0.5725 0.7448 0.8773 0.9558 0.9895 0.9988 1.
    • 0.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0008 0.0027 0.0082 0.0216 0.0507 0.1057 0.1966 0.3264 0.4857 0.6519 0.7974 0.9021 0.9626 0.9894 0.9980 0.9998 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0006 0.0021 0.0064 0.0169 0.0401 0.0845 0.1593 0.2696 0.4112 0.5685 0.7186 0.8405 0.9234 0.9698 0.9907 0.9979 0.9997 1.0000 1.
    • 2/
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0007 0.0025 0.0072 0.0188 0.0435 0.0898 0.1660 0.2761 0.4152 0.5683 0.7140 0.8332 0.9162 0.9645 0.9878 0.9967 0.9993 0.9999 1.0000 1.
    • 0.65 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0014 0.0045 0.0124 0.0301 0.0652 0.1263 0.2198 0.3452 0.4922 0.6425 0.7753 0.8762 0.9414 0.9767 0.9925 0.9981 0.9997 1.0000 1.0000 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0009 0.0029 0.0083 0.0212 0.0481 0.0971 0.1754 0.2855 0.4215 0.5689 0.7085 0.8237 0.9060 0.9565 0.9828 0.9943 0.9985 0.9997 1.0000 1.0000 1.0000 1.
    • 0.55 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0016 0.0050 0.0138 0.0334 0.0714 0.1356 0.2309 0.3552 0.4975 0.6408 0.7673 0.8650 0.9306 0.9688 0.9879 0.9960 0.9989 0.9998 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0007 0.0026 0.0081 0.0214 0.0494 0.1002 0.1808 0.2923 0.4278 0.5722 0.7077 0.8192 0.8998 0.9506 0.9786 0.9919 0.9974 0.9993 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.45 0.0000 0.0000 0.0000 0.0000 0.0002 0.0011 0.0040 0.0121 0.0312 0.0694 0.1350 0.2327 0.3592 0.5025 0.6448 0.7691 0.8644 0.9286 0.9666 0.9862 0.9950 0.9984 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0000 0.0000 0.0000 0.0003 0.0015 0.0057 0.0172 0.0435 0.0940 0.1763 0.2915 0.4311 0.5785 0.7145 0.8246 0.9029 0.9519 0.9788 0.9917 0.9971 0.9991 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.35 0.0000 0.0000 0.0003 0.0019 0.0075 0.0233 0.0586 0.1238 0.2247 0.3575 0.5078 0.6548 0.7802 0.8737 0.9348 0.9699 0.9876 0.9955 0.9986 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0000 0.0001 0.0007 0.0033 0.0122 0.0355 0.0838 0.1668 0.2860 0.4317 0.5848 0.7239 0.8340 0.9102 0.9565 0.9812 0.9928 0.9975 0.9993 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0000 0.0003 0.0021 0.0093 0.0302 0.0766 0.1595 0.2814 0.4315 0.5888 0.7304 0.8407 0.9155 0.9599 0.9831 0.9936 0.9979 0.9994 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.25 0.0002 0.0020 0.0106 0.0374 0.0979 0.2026 0.3481 0.5143 0.6736 0.8034 0.8943 0.9493 0.9784 0.9918 0.9973 0.9992 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0012 0.0105 0.0442 0.1227 0.2552 0.4275 0.6070 0.7608 0.8713 0.9389 0.9744 0.9905 0.9969 0.9991 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 1/
      • 0.0042 0.0295 0.1028 0.2396 0.4243 0.6164 0.7765 0.8863 0.9494 0.9803 0.9933 0.9980 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.15 0.0076 0.0480 0.1514 0.3217 0.5245 0.7106 0.8474 0.9302 0.9722 0.9903 0.9971 0.9992 0.9998 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • 0.0424 0.1837 0.4114 0.6474 0.8245 0.9268 0.9742 0.9922 0.9980 0.9995 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • 0.05 0.2146 0.5535 0.8122 0.9392 0.9844 0.9967 0.9994 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • = n - = x - λ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0. ø = ∑
  • x = 0 0.9900 0.9802 0.9704 0.9608 0.9512 0.9418 0.9324 0.9231 0. - 1 1.0000 0.9998 0.9996 0.9992 0.9988 0.9983 0.9977 0.9970 0. - 2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0. - 3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1. - λ 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.
    • x = 0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0. - 1 0.9953 0.9825 0.9631 0.9384 0.9098 0.8781 0.8442 0.8088 0. - 2 0.9998 0.9989 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0. - 3 1.0000 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0. - 4 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0. - 5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0. - 6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • λ 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.
    • x = 0 0.3679 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0. - 1 0.7358 0.6990 0.6626 0.6268 0.5918 0.5578 0.5249 0.4932 0.4628 0. - 2 0.9197 0.9004 0.8795 0.8571 0.8335 0.8088 0.7834 0.7572 0.7306 0. - 3 0.9810 0.9743 0.9662 0.9569 0.9463 0.9344 0.9212 0.9068 0.8913 0. - 4 0.9963 0.9946 0.9923 0.9893 0.9857 0.9814 0.9763 0.9704 0.9636 0. - 5 0.9994 0.9990 0.9985 0.9978 0.9968 0.9955 0.9940 0.9920 0.9896 0. - 6 0.9999 0.9999 0.9997 0.9996 0.9994 0.9991 0.9987 0.9981 0.9974 0. - 7 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0. - 8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0. - 9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • λ 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.
    • x = 0 0.1353 0.1225 0.1108 0.1003 0.0907 0.0821 0.0743 0.0672 0.0608 0. - 1 0.4060 0.3796 0.3546 0.3309 0.3084 0.2873 0.2674 0.2487 0.2311 0. - 2 0.6767 0.6496 0.6227 0.5960 0.5697 0.5438 0.5184 0.4936 0.4695 0. - 3 0.8571 0.8386 0.8194 0.7993 0.7787 0.7576 0.7360 0.7141 0.6919 0. - 4 0.9473 0.9379 0.9275 0.9162 0.9041 0.8912 0.8774 0.8629 0.8477 0. - 5 0.9834 0.9796 0.9751 0.9700 0.9643 0.9580 0.9510 0.9433 0.9349 0. - 6 0.9955 0.9941 0.9925 0.9906 0.9884 0.9858 0.9828 0.9794 0.9756 0. - 7 0.9989 0.9985 0.9980 0.9974 0.9967 0.9958 0.9947 0.9934 0.9919 0. - 8 0.9998 0.9997 0.9995 0.9994 0.9991 0.9989 0.9985 0.9981 0.9976 0. - 9 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0. - 10 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0. - 11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0. - 12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
      • λ 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.
    • x = 0 0.0498 0.0450 0.0408 0.0369 0.0334 0.0302 0.0273 0.0247 0.0224 0. - 1 0.1991 0.1847 0.1712 0.1586 0.1468 0.1359 0.1257 0.1162 0.1074 0. - 2 0.4232 0.4012 0.3799 0.3594 0.3397 0.3208 0.3027 0.2854 0.2689 0. - 3 0.6472 0.6248 0.6025 0.5803 0.5584 0.5366 0.5152 0.4942 0.4735 0. - 4 0.8153 0.7982 0.7806 0.7626 0.7442 0.7254 0.7064 0.6872 0.6678 0. - 5 0.9161 0.9057 0.8946 0.8829 0.8705 0.8576 0.8441 0.8301 0.8156 0. - 6 0.9665 0.9612 0.9554 0.9490 0.9421 0.9347 0.9267 0.9182 0.9091 0. - 7 0.9881 0.9858 0.9832 0.9802 0.9769 0.9733 0.9692 0.9648 0.9599 0. - 8 0.9962 0.9953 0.9943 0.9931 0.9917 0.9901 0.9883 0.9863 0.9840 0. - 9 0.9989 0.9986 0.9982 0.9978 0.9973 0.9967 0.9960 0.9952 0.9942 0. - 10 0.9997 0.9996 0.9995 0.9994 0.9992 0.9990 0.9987 0.9984 0.9981 0. - 11 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0. - 12 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0. - 13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0. - 14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • λ 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4. CUMULATIVE POISSON PROBABILITIES
  • x = 0 0.0183 0.0166 0.0150 0.0136 0.0123 0.0111 0.0101 0.0091 0.0082 0. - 1 0.0916 0.0845 0.0780 0.0719 0.0663 0.0611 0.0563 0.0518 0.0477 0. - 2 0.2381 0.2238 0.2102 0.1974 0.1851 0.1736 0.1626 0.1523 0.1425 0. - 3 0.4335 0.4142 0.3954 0.3772 0.3594 0.3423 0.3257 0.3097 0.2942 0. - 4 0.6288 0.6093 0.5898 0.5704 0.5512 0.5321 0.5132 0.4946 0.4763 0. - 5 0.7851 0.7693 0.7531 0.7367 0.7199 0.7029 0.6858 0.6684 0.6510 0. - 6 0.8893 0.8786 0.8675 0.8558 0.8436 0.8311 0.8180 0.8046 0.7908 0. - 7 0.9489 0.9427 0.9361 0.9290 0.9214 0.9134 0.9049 0.8960 0.8867 0. - 8 0.9786 0.9755 0.9721 0.9683 0.9642 0.9597 0.9549 0.9497 0.9442 0. - 9 0.9919 0.9905 0.9889 0.9871 0.9851 0.9829 0.9805 0.9778 0.9749 0. - 10 0.9972 0.9966 0.9959 0.9952 0.9943 0.9933 0.9922 0.9910 0.9896 0. - 11 0.9991 0.9989 0.9986 0.9983 0.9980 0.9976 0.9971 0.9966 0.9960 0. - 12 0.9997 0.9997 0.9996 0.9995 0.9993 0.9992 0.9990 0.9988 0.9986 0. - 13 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0. - 14 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0. - 15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0. - 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • λ 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.
  • x = 0 0.0067 0.0041 0.0025 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 0. - 1 0.0404 0.0266 0.0174 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 0. - 2 0.1247 0.0884 0.0620 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 0. - 3 0.2650 0.2017 0.1512 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 0. - 4 0.4405 0.3575 0.2851 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 0. - 5 0.6160 0.5289 0.4457 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0. - 6 0.7622 0.6860 0.6063 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0. - 7 0.8666 0.8095 0.7440 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0. - 8 0.9319 0.8944 0.8472 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0. - 9 0.9682 0.9462 0.9161 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0. - 10 0.9863 0.9747 0.9574 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0. - 11 0.9945 0.9890 0.9799 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0. - 12 0.9980 0.9955 0.9912 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0. - 13 0.9993 0.9983 0.9964 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0. - 14 0.9998 0.9994 0.9986 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0. - 15 0.9999 0.9998 0.9995 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0. - 16 1.0000 0.9999 0.9998 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0. - 17 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0. - 18 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0. - 19 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0. - 20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0. - 21 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0. - 22 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0. - 23 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0. - 24 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
    • λ 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19. CUMULATIVE POISSON PROBABILITIES
  • x = 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0. - 1 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0. - 2 0.0028 0.0012 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0. - 3 0.0103 0.0049 0.0023 0.0011 0.0005 0.0002 0.0001 0.0000 0.0000 0. - 4 0.0293 0.0151 0.0076 0.0037 0.0018 0.0009 0.0004 0.0002 0.0001 0. - 5 0.0671 0.0375 0.0203 0.0107 0.0055 0.0028 0.0014 0.0007 0.0003 0. - 6 0.1301 0.0786 0.0458 0.0259 0.0142 0.0076 0.0040 0.0021 0.0010 0. - 7 0.2202 0.1432 0.0895 0.0540 0.0316 0.0180 0.0100 0.0054 0.0029 0. - 8 0.3328 0.2320 0.1550 0.0998 0.0621 0.0374 0.0220 0.0126 0.0071 0. - 9 0.4579 0.3405 0.2424 0.1658 0.1094 0.0699 0.0433 0.0261 0.0154 0. - 10 0.5830 0.4599 0.3472 0.2517 0.1757 0.1185 0.0774 0.0491 0.0304 0. - 11 0.6968 0.5793 0.4616 0.3532 0.2600 0.1848 0.1270 0.0847 0.0549 0. - 12 0.7916 0.6887 0.5760 0.4631 0.3585 0.2676 0.1931 0.1350 0.0917 0. - 13 0.8645 0.7813 0.6815 0.5730 0.4644 0.3632 0.2745 0.2009 0.1426 0. - 14 0.9165 0.8540 0.7720 0.6751 0.5704 0.4657 0.3675 0.2808 0.2081 0. - 15 0.9513 0.9074 0.8444 0.7636 0.6694 0.5681 0.4667 0.3715 0.2867 0. - 16 0.9730 0.9441 0.8987 0.8355 0.7559 0.6641 0.5660 0.4677 0.3751 0. - 17 0.9857 0.9678 0.9370 0.8905 0.8272 0.7489 0.6593 0.5640 0.4686 0. - 18 0.9928 0.9823 0.9626 0.9302 0.8826 0.8195 0.7423 0.6550 0.5622 0. - 19 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752 0.8122 0.7363 0.6509 0. - 20 0.9984 0.9953 0.9884 0.9750 0.9521 0.9170 0.8682 0.8055 0.7307 0. - 21 0.9993 0.9977 0.9939 0.9859 0.9712 0.9469 0.9108 0.8615 0.7991 0. - 22 0.9997 0.9990 0.9970 0.9924 0.9833 0.9673 0.9418 0.9047 0.8551 0. - 23 0.9999 0.9995 0.9985 0.9960 0.9907 0.9805 0.9633 0.9367 0.8989 0. - 24 1.0000 0.9998 0.9993 0.9980 0.9950 0.9888 0.9777 0.9594 0.9317 0. - 25 1.0000 0.9999 0.9997 0.9990 0.9974 0.9938 0.9869 0.9748 0.9554 0. - 26 1.0000 1.0000 0.9999 0.9995 0.9987 0.9967 0.9925 0.9848 0.9718 0. - 27 1.0000 1.0000 0.9999 0.9998 0.9994 0.9983 0.9959 0.9912 0.9827 0. - 28 1.0000 1.0000 1.0000 0.9999 0.9997 0.9991 0.9978 0.9950 0.9897 0. - 29 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9989 0.9973 0.9941 0. - 30 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9994 0.9986 0.9967 0. - 31 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9993 0.9982 0. - 32 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9990 0. - 33 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0. - 34 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0. - 35 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0. - 36 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0. - 37 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0. - 38 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.
  • p 0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0. P( T ⩽ t ) = p
    • ν = 1 1.000 3.078 6.314 12.71 31.82 63.66 127.3 318.3 636. - 2 0.816 1.886 2.920 4.303 6.965 9.925 14.09 22.33 31. - 3 0.765 1.638 2.353 3.182 4.541 5.841 7.453 10.21 12. - 4 0.741 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8. - 5 0.727 1.476 2.015 2.571 3.365 4.032 4.773 5.894 6. - 6 0.718 1.440 1.943 2.447 3.143 3.707 4.317 5.208 5. - 7 0.711 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5. - 8 0.706 1.397 1.860 2.306 2.896 3.355 3.833 4.501 5. - 9 0.703 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4. - 10 0.700 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4. - 11 0.697 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4. - 12 0.695 1.356 1.782 2.179 2.681 3.055 3.428 3.930 4. - 13 0.694 1.350 1.771 2.160 2.650 3.012 3.372 3.852 4. - 14 0.692 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4. - 15 0.691 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4. - 16 0.690 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4. - 17 0.689 1.333 1.740 2.110 2.567 2.898 3.222 3.646 3. - 18 0.688 1.330 1.734 2.101 2.552 2.878 3.197 3.610 3. - 19 0.688 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3. - 20 0.687 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3. - 21 0.686 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3. - 22 0.686 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3. - 23 0.685 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3. - 24 0.685 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3. - 25 0.684 1.316 1.708 2.060 2.485 2.787 3.078 3.450 3. - 26 0.684 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3. - 27 0.684 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3. - 28 0.683 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3. - 29 0.683 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3. - 30 0.683 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3. - 40 0.681 1.303 1.684 2.021 2.423 2.704 2.971 3.307 3. - 60 0.679 1.296 1.671 2.000 2.390 2.660 2.915 3.232 3.
      • 120 0.677 1.289 1.658 1.980 2.358 2.617 2.860 3.160 3. - ∞ 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.