Question

According to the National Health Survey, systolic blood pressures of 18- to 74-year-old males in the United States are normally distributed with mean 129 millimeters of mercury (mm Hg) and standard deviation 19.8 mm Hg.

Determine the quantile q of the distribution of the systolic blood pressures such that 95% of the population has systolic blood pressure ≤ q.              

Answer 1

Consider, X - Systolic blood pressures of 18 to 75 year-old males
Given that, X~Normal distribution with

Define , , Z is standard normal variate.

1) We have to find q such that P(X<q)=0.95

Using standard normal table, z'=1.64
or,
then, q= 129+1.64*19.8=161.5
So, Quantile q=161.5