SYSTOLIC BLOOD PRESSURE
Math 116 – Reviewing for the Final Exam
This is all about Means
Chapter 6 – Normal Distributions
1) For 18-24 year old women, systolic blood pressures (in mm Hg) are normally distributed with
a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg.
a) Identify the population and the variable.
Population: 18-24 year old women
Variable: systolic blood pressures (in mm Hg)
b) Identify usual and unusual systolic blood pressures for this population according to the
range rule of thumb.
2 114.8 2 *13.1
[88.6,141]
Any systolic blood pressure reading which is outside of the above interval is considered to
be unusual
c) If one woman from this age group is randomly selected, what is the probability that her
systolic blood pressure is
(i) Between 94 and 142 mm Hg?
94 114.8 142 114.8
(94 142) ( )
13.1 13.1
( 1.59 2.07) 0.9808 0.0559 .9249
P x P z
P z
With calculator: normalcdf(94, 142, 114.8, 13.1) = .9249
(ii) At most 82 mm Hg?
82 114.8
( 82) ( ) ( 2.50) 0.0062
13.1
P x P z P z
With calculator: normalcdf(-10^9, 82, 114.8, 13.1) = 0.0061
(iii) At least 143 mm Hg?
143 114.8
( 143) ( ) ( 2.15) 1 .9842 .0158
13.1
P x P z P z
With calculator: normalcdf(143, 10^9, 114.8, 13.1) = 0.0157
d) Find the two blood pressures having these properties: the mean is midway between them
and 90% of all blood pressures are between them.
There are two scores, one separating the top 5% (with an area of .95 to its left), and
another separating the bottom 5% (with an area of 0.05 to its left). Use the table, from
inside out to find the z scores. The z-scores are – 1.645, and 1.645. Then, use the formula:
114.8 1.645*13.1 93.25
114.8 1.645*13.1 136.35
x z
x z
With calculator: invNorm(0.05, 114.8, 13.1) = 93.25
With calculator: invNorm(0.95, 114.8, 13.1) = 136.35
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