Answer
a. $\mu = 6$
$\sigma = 2.16$
b. 4,5 ; 4.5
5,5; 5
9,5; 7
5,9; 7
4,9;6.5
9,9; 9
4,4; 4
4,9; 6.5
c. 1.08
d. The result is the same as in part c.
Work Step by Step
a. We find that the mean is:
$\mu =\frac{4+5+9}{3}=6$
We know the following equation for the standard deviation:
$\sigma = \sqrt{\frac{\Sigma(x-\bar{x})^2}{n}}$
Using the proper values, it follows that $\sigma = 2.16$.
b. We consider all of the possible samples:
Sample; mean
4,5 ; 4.5
5,5; 5
9,5; 7
5,9; 7
4,9;6.5
9,9; 9
4,4; 4
4,9; 6.5
c. We find that the mean is:
$\bar{\mu} =6$
We use the equation $\sigma = \sqrt{\frac{\Sigma(x-\bar{x})^2}{n}}$, where n=6, to find that the standard deviation is 1.080.
d. We plug in the known values into the equation $\frac{\sigma}{\sqrt{n}}\sqrt{\frac{N-n}{N-1}}$ to obtain a value of 1.08. This is the same as the value that we found in part c.
