Question

Suppose the heights of males on campus are normally distributed with a mean of 69 inches and standard deviation of 2.5 inches. You plan to choose a random sample of 14 males from the studer directory a. What is the probability the mean height for your sample will be greater than 70.5 inches? b. The sample size you used was fairly small. Does this affect the validity of the probability you calculated in (a)? Explain fully!

Answer 1

(a)

Mean = mu = 69

SD = sigma = 2.5

n = 14

SE = sigma/ sqrt(n)

= 2.5/sqrt(14)

= 0.6682

To find P(xbar > 70.5):

Z = (70.5 - 69)/0.6682

= 2.2450

By Technology, Cumulative Area Under Standard Normal Curve = 0.9876

So,

P(xbar > 70.5):= 1 - 0.9876 = 0.0124

So,

Answer is:

0.0214

(b)

Since population is given as Normally distribute and population Standard deviation is given, even though Sample Size = n = 14 < 30, small sample, the sampling distribution of sample mean will be normal distribution.

So,

Answer is:

This does not affect the probability calculations in (a)