Question

assume that females have pulse rates that are normally distributed with a mean of $mu = 72.0$ beats per minute and a standard deviation of $sigma = 12.5$ beats per minute. complete parts (a) through (c) below.
a. if 1 adult female is randomly selected, find the probability that her pulse rate is less than 76 beats per minute.
the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 76$, $\mu=72$, and $\sigma = 12.5$.
$z=\frac{76 - 72}{12.5}=\frac{4}{12.5}=0.32$

Step2: Find the probability from the standard normal distribution table

We want to find $P(X<76)$, which is equivalent to $P(Z < 0.32)$ in the standard - normal distribution. Looking up the value of $0.32$ in the standard normal distribution table, we get $P(Z < 0.32)=0.6255$.

Answer:

$0.6255$