Question

Assume that females have pulse rates that are normally distributed with a mean of μ 76.0 beats per minute and a standard deviation of σ 12.5 beats per min Complete parts (a) through (c) below a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute. The probablity is .5948 0 (Round to four decimal places as needed.) b. IH 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute The probablity is (Round to four decimal places as needed.)

Answer 1

a) The probability that the pulse rate of a randomly selected adult female is less than 79 beats per minute is approximately 0.5948.

b) If 16 adult females are randomly selected, the probability that their mean pulse rate is less than 79 beats per minute can be calculated using the Central Limit Theorem.

Step-by-step explanation:

a) To find the probability that the pulse rate of a single randomly selected adult female is less than 79 beats per minute, we use the standard normal distribution. With a mean (\(\mu\)) of 76.0 and a standard deviation (\(\sigma\)) of 12.5, we calculate the z-score for 79 and use a standard normal distribution table or calculator to find the corresponding probability, which is approximately \(0.5948\) rounded to four decimal places.

b) When dealing with the mean pulse rate of a sample of 16 adult females, we can use the Central Limit Theorem. Given that the sample size is sufficiently large (n = 16), the distribution of sample means will be approximately normal. We apply the same principles as in part (a) to find the probability that the mean pulse rate of the sample is less than 79 beats per minute.