Chapter 6.1, Problem 13E

To determine

To find: the standard deviation of Y and explain it

Answer to Problem 13E

  $\sigma =6.429$

Explanation of Solution

Given:

Probability(Y)	0	5	10	15	20	25
Probability	0.02	0.05	0.08	0.16	0.27	0.42

Formula used:

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

Calculation:

y	$\text{P}\left(y\right)$	$\text{yP}\left(y\right)$	$y^2$	$y^2\text{P}\left(y\right)$
0	0.02	0	0	0
5	0.05	0.25	25	1.25
10	0.08	0.8	100	8
15	0.16	2.4	225	36
20	0.27	5.4	400	108
25	0.42	10.5	625	262.5
		19.35		415.75

  $\begin{array}{c}E\left(Y\right)={\displaystyle \sum yP(y)}\\ =19.35\\ E\left(Y^2\right)=y^{2}P\left(y\right)\\ =415.75\end{array}$

  $\begin{array}{c}\sigma =\sqrt{415.75-{19.35}^2}\\ =\sqrt{41.327}\\ =6.429\end{array}$

Standard deviation is $6.43 and mean is $19.35 therefore the collection of amount on a arbitrary choose varies $6.43 from the mean amount of money collected $19.35