Answer to Question #327789 in Statistics and Probability for AKIRA

Question

> Find the mean of the population

> Find the mean of the sampling distribution of the

sample means

> find the Variance of the population

> find the Variance of the sampling distribution of the

sample mean

> find the Standard deviation of the population

> find the Standard deviation of the sampling

distribution of the sample mean

STUDENT HEIGHT (IN CM)

A 120

B 130

C 110

D 125

E 159

Answer 1

$\mu =\frac{120+130+110+125+159}{5}=128.8\\\mu _{\bar{x}}=\mu =128.8\\\sigma ^2=\frac{\left( 120-128.8 \right) ^2+\left( 130-128.8 \right) ^2+\left( 110-128.8 \right) ^2+\left( 125-128.8 \right) ^2+\left( 159-128.8 \right) ^2}{5}=271.76\\{\sigma ^2}_{\bar{x}}=\frac{\sigma ^2}{n}=\frac{271.76}{n}\\\sigma =\sqrt{\sigma ^2}=\sqrt{271.76}=16.4851\\\sigma _{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{16.4851}{\sqrt{n}}$