Answer to Question #221728 in Statistics and Probability for Ryan

Question

Assume that females have pulse rates that are normally distributed with a mean of μ=76.0 beats per minute and a standard deviation of σ=12.5 beats per minute. a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 69 beats per minute and 83 beats per minute. The probability is (Round to four decimal places as needed.)

Answer 1

Solution:

We are given that females have pulse rates that are normally distributed with

$$\mu=76, \sigma=12.5.$$ $$z={{\overline{x}-\mu} \over {\sigma / \sqrt{n}}}$$ $$z={{\overline{x}-76} \over {12.5 / \sqrt{1}}}={{\overline{x}-76} \over {12.5 }}$$ $$P(69<\overline{x}<83)=P(\overline{x}<83)-P(\overline{x}<69)$$ $$=P(z<{{83-76} \over {12.5 }})-P(z<{{69-76} \over {12.5 }}) \\=P(z<0.56)-P(z<-0.56)=P(z<0.56)-[1-P(z\le0.56)] \\=2\times0.71226-1 \\=0.42452$$