Question

assume that females have pulse rates that are normally distributed with a mean of μ = 73.0 beats per minute and standard deviation of σ = 12.5 beats per minute. complete parts (a) through (c) below.
the probability is 0.8315.
(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 individuals, not sample means, the distribution 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 original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Explanation:

The Central Limit Theorem states that if the original population is normally distributed, then the distribution of sample means is also normally distributed for any sample size. In this case, the original population (female pulse rates) is given as normally distributed. Options A and B are incorrect as they misstate the relevant concepts. Option C is also incorrect.

Answer:

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