Part 1 of 3 Points: 0 of 1 Save 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 $\square$. (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 \(\boxed{0.5948}\).