Answer to Question #223839 in Statistics and Probability for Magy

Question

consider a population of 5-lb sacks of potatoes for which the variable of interest is the number of potatoes,for which the variable of interest is the number of potatoes.It is a discrete uniform distribution on the intergers 12 through 18.

find the mean ,variance ,and standard deviation of this sampling distribution of the mean for n=2

Answer 1

The sampling distribution of the sample mean is as follows:

Mean of the sample mean,

$E\left(\overline{x}\right)=\sum \:\overline{x}P\left(\overline{x}\right)=15$

$E\left(\overline{x}^2\right)=\sum \:\overline{x}^2P\left(\overline{x}\right)=227$

$Var\left(\overline{x}^2\right)=E\left(\overline{x}^2\right)-\left[E\left(\overline{x}\right)\right]^2$

$Var\left(\overline{x}^2\right)=227-15^2=2$

Standard deviation of $\overline{x}=SD\left(\overline{x}\right)=\sqrt{Var\left(\overline{x}^2\right)}$

$SD\left(\overline{x}\right)=\sqrt{2}\approx 1.414$