Question

# The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm202.5...

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

202.5 cm202.5 cm

and a standard deviation of

8.9 cm8.9 cm.

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

212.50212.50

cm.b. Find the probability that the mean for

2525

randomly selected distances is greater than 201.20 cm.201.20 cm.

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

a. The probability is

nothing.

​(Round to four decimal places as​ needed.)

b. The probability is

nothing.

​(Round to four decimal places as​ needed.)

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 original population has a normal distribution.

C.

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

D.

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

The probability is 0.7674

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

Ans:-  B. The normal distribution can be used because the original population has a normal distribution.