Chapter 6.1, Problem 14E

To determine

To find: the standard deviation of Y

Answer to Problem 14E

  $\sigma =12.632$

Explanation of Solution

Given:

Score(Y)	10	20	30	40	50
Probability	0.32	0.27	0.19	0.15	0.07

Formula used:

  $\sigma =\sqrt{E\left(Y^2\right)+{\left\{E\left(Y\right)\right\}}^2}$

Calculation:

y	$\text{P}\left(y\right)$	$\text{yP}\left(y\right)$	$y^2$	$y^2\text{P}\left(y\right)$
10	0.32	3.2	100	32
20	0.27	5.4	400	108
30	0.19	5.7	900	171
40	0.15	6	1600	240
50	0.07	3.5	2500	175
		23.8		726

  $\begin{array}{c}E\left(Y\right)={\displaystyle \sum yP(y)}\\ =23.8\\ E\left(Y^2\right)=y^{2}P\left(y\right)\\ =726\end{array}$

  $\begin{array}{c}\sigma =\sqrt{726-{23.8}^2}\\ =\sqrt{726-566.44}\\ =\sqrt{159.56}\\ =12.632\end{array}$

Standard deviation is 12.632 and mean is 23.8 therefore the scores on an arbitrary choose varies 12.632 from the mean days 23.8