Assume that females have pulse rates that are normally distributed with a mean of 75.0 bpm and a standard deviation of 12.5 bpm complete parts a through C.
below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 82 beats per minute.
The probability is
(Round to four decimal places as needed.)
Answer
Final Answer: The probability that the pulse rate of a randomly selected adult female is less than 82 beats per minute is approximately \(\boxed{0.7123}\).
Step 1 ：We are given that females have pulse rates that are normally distributed with a mean of 75.0 bpm and a standard deviation of 12.5 bpm.
Step 2 ：We are asked to find the probability that a randomly selected adult female has a pulse rate less than 82 beats per minute.
Step 3 ：To solve this, we use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.
Step 4 ：We calculate the Z-score for 82 beats per minute using the formula \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the value we are interested in (82 bpm), \(\mu\) is the mean (75.0 bpm), and \(\sigma\) is the standard deviation (12.5 bpm).
Step 5 ：Substituting the given values into the formula, we get a Z-score of approximately 0.56.
Step 6 ：We then look up this Z-score in the standard normal distribution table to find the probability. The probability corresponding to a Z-score of 0.56 is approximately 0.7123.
Step 7 ：This means that there is a 71.23% chance that a randomly selected adult female will have a pulse rate of less than 82 beats per minute.
Step 8 ：Final Answer: The probability that the pulse rate of a randomly selected adult female is less than 82 beats per minute is approximately \(\boxed{0.7123}\).
