Question

the following are the height of 8 students in centimeters suppose sampe of size 3 are taken from this population of 8 students.

student height

a 120

b 130

c 110

d 125

e 152

f 170

g 137

h 155

a) how many sample are possible? list them and cmpute the mean of each example?

b) construct the sampling distribution of the sample means

c) construct the histogram of the sampling distribution of the sample means

Answer 1

a. Number of samples$C^3_8=\frac{8!}{3!5!}=56$

$Mean=(x_1+x_2+x_3)/3$

Frequency is how much this mean contains in the 56 samples size 3.

Probability=Frequency (X)/Number of samples.

$E(x)=\sum Probability (X)Mean(X)=133.7$

$\sigma=\sum Probability (X)Mean(X)^2-(\sum Probability (X)Mean(X))^2=38.3$