Question

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

205 cm

and a standard deviation of

8.9 cm

.

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

214.30

cm.

b. Find the probability that the mean for

20

randomly selected distances is greater than 203.70 cm.

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

a. the proabibility is ___.

b. the probability is ____.

c. Choose the correct answer below.

A.

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

B.

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

C.

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

D.

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

Answer 1

Solution: Given that mean = 205, sd = 8.9

a. P(X > 214.30) = P((X-mean)/sd > (214.30-205)/8.9)
= P(Z > 1.0449)
= 0.1492

b. For n = 20
P(X > 214.30) = P((X-mean)/(sd/sqrt(n)) > (214.30-205)/(8.9/sqrt(20)))
= P(Z > 4.6731)
= 1-1
= 0

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