Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 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 75 beats per minute.

The probability is _________

(Round to four decimal places as needed.)

b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 75 beats per minute.

The probability is _________

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

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

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

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

Answer 1

µ = 72

sd = 12.5

a)

                            

                             = P(Z < 0.24)

                             = 0.5948

b)

                              

                               = P(Z < 0.48)

                               = 0.6844

c) Option-D) Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.