Question

4. For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed
with a mean of 114.8 and a standard deviation of 12.6 (based on data from the National Health
Survey).
(a) If one woman in that age bracket is randomly selected, find the probability that her systolic
blood pressure is less than 110.

(b) If 20 women in that age bracket are randomly selected, describe the sampling distribution of
the sample mean x , the mean systolic blood pressure for the sample of 20 women. Use clear,
complete sentences to state and justify your answers.

(c) For the sample of 20 women, find the probability that their mean systolic blood pressure is
less than 110.

(d) Use clear, complete sentences to explain the difference between your answers in part (a) and
part (c). If you got the same answer, explain why they are the same answer. If you got different
answers, explain why they are different.

Answer 1

4. Here it is given that distribution is normal with mean=114.8 and sd=12.6

a. Now we need to find

As distribution is normal we can convert x to z

b. For sample size n=20, but population is normal so as per central limit theorem distribution of sample mean is normal with mean

Mean is and

c. Now we need to find

As sample mean is normal we can convert sample mean to z

d. As for a we have used the whole population, but when we use only few samples probability decreases.