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.)

Step 1 ：Given that the pulse rates of females are normally distributed with a mean of \(\mu = 72.0\) beats per minute and a standard deviation of \(\sigma = 12.5\) beats per minute.

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

Step 3 ：To solve this, we first calculate the Z-score, which is the number of standard deviations a data point is from the mean. The formula for the Z-score is \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the value we are interested in.

Step 4 ：Substituting the given values into the formula, we get \(Z = \frac{76 - 72.0}{12.5} = 0.32\).

Step 5 ：We then use the cumulative distribution function (CDF) of the normal distribution to find the probability that a randomly selected adult female has a pulse rate less than 76 beats per minute. The CDF gives us 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 0.6255.

Step 7 ：Final Answer: The probability that a randomly selected adult female has a pulse rate less than 76 beats per minute is approximately \(\boxed{0.6255}\).