Answer to Question #138538 in Statistics and Probability for Sarahi

Question

Assume that females have pulse rates that are normally distributed with a mean of 72.0 beats per minute and a standard deviation of 12.5 beats per minute.
if 1 adult female is randomly​ selected, find the probability that her pulse rate is between 65 beats per minute and 79 beats per minute.

Answer 1

Let's denote mean $a = 72,$ standard deviation $\sigma = 12.5$.

We will use the formula:

$P(|x-a|< \epsilon) = 2Ф(\cfrac{\epsilon}{\sigma})$ , where $Ф$ denotes cumulative distribution function for normal distribution.

Thus:

$P(65<x<79) = P(|x-72|<7)=2Ф(\cfrac{7}{12.5}) \approx 0.4246$