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```SYSTOLIC BLOOD PRESSURE
Chapter 7 – Section 7.2 – Distribution of Sample Means
2) For women aged 18-24, 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) Give the shape, mean and standard deviation of the distribution of sample means for samples
of size 36.
Notice: the population is 18-24 year old women and the variable X is their systolic blood
pressure (in mm Hg)
X is Normal with   114.8 and   13.1
According to the Central Limit Theorem, the distribution of sample means is normal for
any sample size because X is normally distributed. Hence, for samples of size 36, the
distribution of x-bar is also normal with
 x    114.8
x 

n

13.1
 2.18
36
b) What is the probability that a sample of 36 women of this age group has a mean systolic blood
pressure of at least 121 mm Hg?
121  114.8
)  P( z  2.84)  1  .9977  .0023
13.1
36
13.1
2
With calculator: normalcdf(121, 109 , 114.8,
) = 0.0023~0.002=
1000
36
P( x  121)  P( z 
A mean of 121 would be more likely in a population with mean higher than 114.8, that is
why we conclude....see ****
c) If the population mean is 114.8, the probability of obtaining a sample of size 36 with a mean
of 121 or more is __0.002_____.
So, for samples of size 36, about __2__ samples in 1000 will have a sample mean of 121 or more
when the population mean is 114.8.
Because this event only happens _2__ out of __1000____ times, we consider it to be
usual/unusual.
d) What may this result suggest?
If the population mean is 114.8, it’s very unusual to observe a sample of size 36 with a
mean of 121 or more. ***********This unusually high result may suggest that “probably”
the sample was selected from a population with mean higher than 114.8.
1
```