Answer
a) $μ=6$
$σ=2.16$
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:
$μ=\frac{4+5+9}{3}=6$
We know the following equation for the standard deviation:
$σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}$
Using the proper values, $σ=2.16$.
b) We take into consideration all 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:
$\overline{μ}=6 $
We use the equation $σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}$, in which $n=6$, to find that the standard deviation is equal to $1.080$.
d. We plug in the known values into $σ=\sqrt{n}\sqrt{\frac{N-n}{N-1}}$ to get a value of 1.08. This is the same as the value that we found in part c).
