Answer to Question #150596 in Statistics and Probability for Vladimyr Lubin

Question

(6.4.7) Assume that females have pulse rates that are normally distributed with a mean of mu=76.0 beats per minute and a standard deviation of sigma=12.5 beats per minute.
a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 72 beats per minute and 80 beats per minute.
The probability is

Answer 1

Let $X=$ pulse rate: $X\sim N(\mu, \sigma^2)$

Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$

Given $\mu=76.0, \sigma=12.5$

$$P(72<X<80)=P(X<80)-P(X\leq72)$$

$$=P(Z<\dfrac{80-76}{12.5})-P(Z\leq\dfrac{72-76}{12.5})$$

$$=P(Z<0.32)-P(Z\leq-0.32)\approx$$

$$\approx0.625516-0.374484=0.251032$$

The probability is $0.251032.$