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.
Part 1
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:
(Round to four decimal places as needed.)
Part 2
b. If 16 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.)
Part 3
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
A. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
B. Since the mean pulse rate exceeds 30, the distribution of sample means 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 distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.