Download Problems in Quiz on Elementary Probability and Statistics | MATH 1530 and more Quizzes Probability and Statistics in PDF only on Docsity!
MATH 1530 – Quiz # 11 (Quizpak 5) Name _____________________________
Assume that the readings on thermometers are normally distributed with a mean of 0 ^ C and a standard deviation of (^) 1.00 ^ C. One thermometer is randomly selected and tested. In each case, label and shade the graph , then find the probability of getting the stated readings in degrees Celsius. Show the areas to be added or subtracted as read from Table A-2 as well as the solution.
1. Between 1.
and 2.
P ( 1.22 z 2.12 )
= ___________________________ = ______________
2. Between 2.
and 2.
P (2.1 z 2.8 )
= ___________________________ = ______________
3. Less than 1.
P z ( 1.34 )
= ___________________________ = ______________
4. Greater than 1.
P z ( 1.56 )
= ___________________________ = ______________
0 z 0 z 0 z 0 z
MATH 1530 – Quiz # 12 (Quizpak 5) Name _____________________________
Find the missing “z-value” given each of the following probabilities come from a Standard Normal Distribution. In each case, label and shade the graph writing the appropriate probabilities over the shaded region, then state the z-score that provides those probabilities as your solution.
1. If P (0^^ ^ z^ ^ a )^ .4370^ , then a^ = _____________.
2. If P b (^^ ^ z ^ 0)^ .3770^ , then b^ = _____________.
3. If P (^^ ^ c^ ^ z^ ^ c )^ .5222^ , then c^ = _____________
and ^ c = _____________.
4. If P z (^^ ^ d )^ .0287^ , then d^ = _____________.
0 z 0 z 0 z 0 z
Given a normally distributed population with mean ^ ^100 and standard deviation 20 , find each of the following scores. Label the graphs accordingly. Show formulas and calculations below the graphs.
1. The score that separates the top 40% from the bottom 60%. ______________
2. The score that separates the bottom 10% from the top 90%. ______________
3. The score that separates the top 10% from the bottom 90%. ______________
4. The score that determines the cut-off for the top 25%. ______________
MATH 1530 – Quiz # 15 (Quizpak 5) Name _____________________________
0 z 100 x 0 z 100 x 0 z 100 x 0 z 100 x
Assume that women’s heights are normally distributed with a mean of ^ 63.6^ inches and a standard deviation 2.5 inches (based on data from the National Health Survey).
1. If 1 woman is selected at random, find the probability that her height is above 63
inches.
P( ) = P( ) = ________________________ = _______________
2. If 100 women are selected at random, find the probability that their mean height is
greater than 63 inches.
P( ) = P( ) = ________________________ = _______________
3. Consider the sampling distribution of randomly selecting 100 women at a time and
recording the mean heights, then this distribution of sample means has a mean and a
standard deviation that are equal to:
(give the numerical values here) x^ = _______________
x = _______________
MTH 1050 – STATDISK WORKSHEET - CHAPTER 5 Name _______________________
( seed = 5 ) Standard Deviation: __________ Distribution shape: _______________________________ Sketch histogram here. b. Two Dice: Mean: __________ ( seed = 5 ) Standard Deviation: __________ Distribution shape: _______________________________ Sketch histogram here. c. 10 Dice: Mean: __________ ( seed = 5 ) Standard Deviation: __________ Distribution shape: _______________________________ Sketch histogram here. d. 20 Dice: Mean: __________ ( seed = 5 ) Standard Deviation: __________ Distribution shape: _______________________________ Sketch histogram here. e. General conclusions: What happens to the mean as the sample size increases from 1to 2 to 10 to 20?
What happens to the standard deviation as the sample size increases?
What happens to the distribution shape as the sample size increases?
How do these results illustrate the central limit theorem?
The following notes will be provided for your reference as the last page of Exam 3:
The Standard Normal Distribution is a normal probability distribution that has a mean
of ^ ^0 and a standard deviation of ^ ^1. (Utilize Table A-2 to find probabilities for
given z-scores or to find z-scores for given probabilities.)
Formula for converting x-scores to z-scores:
x
z
Formula for converting z-scores to x-scores:
x ( z )
The Central Limit Thereom:
For large sample sizes (n>30) drawn from ANY distribution (or for smaller sample
sizes, if the original distribution is normally distributed), the sampling distribution of the
means has the following properties:
1. The distribution of the sample means is approximately Normal.
2. The mean of the sampling distribution is equal to the mean of the population.
x
3. The standard deviation of the sampling distribution is equal to the standard
deviation of the population divide by the square root of n.
x
n
