The overhead reach distances of adult females are normally distributed with a mean of

195cm

and a standard deviation of

7.8cm.

a. Find the probability that an individual distance is greater than

208.40

cm.

b. Find the probability that the mean for

15

randomly selected distances is greater than 193.50cm.

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

Question content area bottom

Part 1

a. The probability is

enter your response here.

(Round to four decimal places as needed.)

Part 2

b. The probability is

enter your response here.

(Round to four decimal places as needed.)

Part 3

c. Choose the correct answer below.

A.

The normal distribution can be used because the finite population correction factor is small.

B.

The normal distribution can be used because the mean is large.

C.

The normal distribution can be used because the original population has a normal distribution.

D.

The normal distribution can be used because the probability is less than 0.5