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 0.5948 .
(Round to four decimal places as needed.)
b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.
The probability is
(Round to four decimal places as needed.)
Answer
Final Answer: The probability that a randomly selected female has a pulse rate less than 76 beats per minute is approximately \(\boxed{0.5948}\).
Step 1 ：We are given that the mean pulse rate of females is \(\mu = 73.0\) beats per minute and the standard deviation is \(\sigma = 12.5\) beats per minute.
Step 2 ：We are asked to find the probability that a randomly selected female has a pulse rate less than 76 beats per minute.
Step 3 ：This is a problem of normal distribution. We can use the z-score formula to find the z-score for 76, which 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 \(z = \frac{76 - 73}{12.5} = 0.24\).
Step 5 ：We can then use a z-table to find the probability that a z-score is less than the calculated value. The probability is approximately 0.5948.
Step 6 ：Final Answer: The probability that a randomly selected female has a pulse rate less than 76 beats per minute is approximately \(\boxed{0.5948}\).
