Using the Central Limit Theorem · Try It 3

Based on data from the National Health Survey, women between the ages of 18 and 24 have an average systolic blood pressures (in mm Hg) of 114.8 with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18 to 24 follows a normal distribution.

(a) If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than 120.
(b) If 40 women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than 120.
(c) If the sample was four women between the ages of 18–24 and we did not know the original distribution, could the central limit theorem be used?

OpenStax, Statistics · §7.3 Using the Central Limit Theorem · Try It 3