# Assume that females have pulse rates that are normally distributed with a mean of 74. 0 beats per minute and a standarddeviation of 12.5 beats per minute. If 1 adult female is randomly selected, find the probability that her pulse rate is greaterthan 70 beats per minute.

preprekomW 2021-08-18 Answered
Assume that females have pulse rates that are normally distributed with a mean of 74. 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 greater than 70 beats per minute.

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## Expert Answer

brawnyN
Answered 2021-08-19 Author has 9868 answers

Given: $$\displaystyle\mu={74.0}$$
$$\displaystyle\sigma={12.5}$$
The standardized score is the value x decreased by the mean and then divided by the standard deviation. $$\displaystyle{z}={\frac{{{x}-\mu}}{{\sigma}}}={\frac{{{70}-{74.0}}}{{{12.5}}}}\approx-{0.32}$$
Determine the corresponding probability using the normal probability table in the appendix: $$\displaystyle{P}{\left({X}{>}{70}\right)}={P}{\left({Z}\succ{0.32}\right)}={1}-{P}{\left({Z}{<}-{0.32}\right)}={1}-{0.3745}={0.6255}$$

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