Answer to Question #324507 in Statistics and Probability for sherelyn obor

Question

1. A population consists of the four numbers (2,3,5). Consider all possible samples of size 2 that can be drawn with

replacement from this population. Find the following:

The mean of the population

b. The standard deviation of the population

The mean of the sampling distribution of means

d. The standard deviation of the sampling distribution of means.

Illustrate the probability histogram of the sampling distribution of the means

Complete the table below.

Answer 1

$a:\\\mu =\frac{2+3+5}{3}=\frac{10}{3}\\b:\\\sigma =\sqrt{\frac{\left( 2-\frac{10}{3} \right) ^2+\left( 3-\frac{10}{3} \right) ^2+\left( 5-\frac{10}{3} \right) ^2}{3}}=1.24722\\c:\\\left( 2,3 \right) ,\bar{x}=2.5\\\left( 2,5 \right) ,\bar{x}=3.5\\\left( 3,5 \right) ,\bar{x}=4\\\mu _{\bar{x}}=\frac{2.5+3.5+4}{3}=\frac{10}{3}\\d:\\\sigma _{\bar{x}}=\sqrt{\frac{\left( 2.5-\frac{10}{3} \right) ^2+\left( 3.5-\frac{10}{3} \right) ^2+\left( 4-\frac{10}{3} \right) ^2}{3}}=0.62361$