Answer to Question #186669 in Statistics and Probability for Acierlynx

Question

Solve the following problems. Use the properties of the sampling distribution of

sample means.

5. If a population with size 3 has a standard deviation of 2.4, what is thestandard 

deviation of the sampling distribution of its means? The sampling distribution 

has a sample size of 2 and all possible samples are drawn without

replacements.

Answer 1

Solution:

given, population size: N=3

$\sigma$ = 2.4

sample size: n=2

Hence,

the standard deviation of the sampling distribution of its means= SD($\bar x$ )=$\dfrac{\sigma}{\sqrt n}$ =$\dfrac{2.4}{\sqrt 2}$ =1.6971

The standard deviation of the sampling distribution of sample mean=1.6971