The overhead reach distances of adult females are normally distributed with a mean of 205.5cm and a standard deviation of 8.9cm.

a. Find the probability that an individual distance is greater than 214.80 cm.

b. Find the probability that the mean for 25 randomly selected distances is greater than 203.30cm.

c. Why can the normal distribution be used in part(b), even though the sample size does not exceed30?

a. The probability is

.

(Round to four decimal places asneeded.)

b. The probability is

.

(Round to four decimal places asneeded.)

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 probability is less than 0.5

C.

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

D.

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