Answer to Question #332454 in Statistics and Probability for Aiz

Question

There are five card in a box containing the numbers 1,3,5,7 and 9. A sample of size 3 is to be drawn at a time. Construct the sampling distribution of the mean.

a.) How many possible samples can be drawn?

b.) List all the possible samples and the corresponding means.

c.) Construct the sampling distribution of the sample means.

d.) Draw the histogram for the sampling distribution of the sample means.

e.) What is the shape of the histogram of the sampling distribution of the sample means?

Answer 1

a. $C^3_5=\frac{5!}{3!2!}=10$

b.m(1,3,5)=(1+3+5)/3=3

m(1,3,7)=(1+3+7)/3=3.7

m(1,3,9)=(1+3+9)/3=4.3

m(1,5,7)=(1+5+7)/3=4.3

m(1,5,9)=(1+5+9)/3=5

m(1,7,9)=(1+7+9)/3=5.7

m(3,5,7)=(3+5+7)/3=5

m(3,5,9)=(3+5+9)/3=5.7

m(5,7,9)=(5+7+9)/3=7

m(3,7,9)=(3+7+9)/3=6.3

c. Frequencies

F(3)=F(3.7)=F(7)=F(6.3)=1

F(4.3)=F(5)=F(5.7)=2

Probabilities $P(x)=F(x)/\sum F(x)$

P(3)=P(3.7)=P(7)=P(6.3)=0.1

P(4.3)=P(5)=P(5.7)=0.2

Histogram has a form of normal distribution