Question

Assume that females have pulse rates that are normally distributed with a mean of

mu equals 75.0μ=75.0

beats per minute and a standard deviation of

sigma equals 12.5σ=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

8181

beats per minute.The probability is

nothing.

​(Round to four decimal places as​ needed.)

b. If

44

adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than

8181

beats per minute.The probability is

nothing.

​(Round to four decimal places as​ needed.)

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

A.

Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

B.

Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

C.

Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.

D.

Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.

Answer 1

C.

B. Since the original population has a normal distribution , the distribution of sample means is a normal distribution for any sample size .