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Assume that females have pulse rates that are normally distributed with a mean of $\mu =73.0$ 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.)

Step 1 ：Given that the pulse rates of females are normally distributed with a mean of $\mu =73.0$ beats per minute and a standard deviation of $\sigma =12.5$ beats per minute.

Step 2 ：We are asked to find the probability that the pulse rate of a randomly selected adult female is less than 76 beats per minute.

Step 3 ：To solve this, we first calculate the Z score. The Z score is a measure of how many standard deviations an element is from the mean. It is calculated as $Z=\frac{X-\mu }{\sigma }$, where X is the value from the dataset (in this case, 76).

Step 4 ：Substituting the given values, we get $Z=\frac{76-73.0}{12.5}=0.24$.

Step 5 ：We then use the cumulative distribution function (CDF) to calculate the probability. The CDF gives the probability that a random variable is less than or equal to a certain value.

Step 6 ：Using the calculated Z score, we find that the probability is approximately 0.5948.

Step 7 ：Therefore, the probability that a randomly selected adult female has a pulse rate less than 76 beats per minute is $\boxed{{\displaystyle 0.5948}}$.