Question

You are a manager responsible for a quality of the product. According to the design spec of the product, the weights of units should be distributed with mean 50 pounds and standard deviation 24 pounds. This distribution is not a Normal distribution. Now, suppose you pick 36 units randomly and check the average weight of these 36 units. You repeat this process many times and obtain a distribution. What is the distribution of the average weights?

A

Not a Normal distribution

B

Normal distribution with mean 50 and standard deviation 10

C

Normal distribution with mean 50 and standard deviation 4

D

Normal distribution with mean 50 and standard deviation 6

E

Normal distribution with mean 50 and standard deviation 12

Answer 1

Solution :

Given that,

The sampling distribution of mean is ,

= 50

The sampling distribution of standard deviation is ,  

= / n = 24 / 36 = 4

C Normal distribution with mean 50 and standard deviation 4 .