Chapter 6.1, Problem 17E

(a)

To determine

To Explain: then company bear a loss when a client dies at age 25

Explanation of Solution

Given:

Age at death	21	22	23	24	25	26 or more
Profit	-$99750	-$99500	-$99250	-$99000	-$98750	$1250
Probability	0.00183	0.00186	0.00189	0.00191	0.00193	0.9958

Company has collected $1250 and at the time of client dies has to pay $100000. So company loss is 100000-1250=98750

(b)

To determine

To Calculate: the expected value and explain it

Answer to Problem 17E

  ${\mu }_Y=E\left(Y\right)=303.35$

Explanation of Solution

Formula used:

  $E\left(Y\right)={\displaystyle \sum yP(y)}$

Calculation;

y	$\text{P}\left(y\right)$	$\text{yP}\left(y\right)$	$y^2$	$y^2\text{P}\left(y\right)$
-99750	0.00183	-182.543	9950062500	18208614
-99500	0.00186	-185.07	9900250000	18414465
-99250	0.00189	-187.583	9850562500	18617563
-99000	0.00191	-189.09	9801000000	18719910
-98750	0.00193	-190.588	9751562500	18820516
1250	0.99058	1238.225	1562500	1547781
		303.3525		94328849

  $\begin{array}{c}E\left(Y\right)={\displaystyle \sum yP(y)}\\ =303.35\end{array}$

By the given data mean is 303.35 so per person $303.35 average money would make by the company

(c)

To determine

To Calculate: the standard deviation of Y and explain it

Answer to Problem 17E

  $\sigma =9707.57$

Explanation of Solution

Formula used:

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

Calculation:

  $\begin{array}{c}E\left(Y^2\right)=y^{2}P\left(y\right)\\ =94328849\end{array}$

  $\begin{array}{c}\sigma =\sqrt{94328849-{303.35}^2}\\ =\sqrt{94328849-92021.22}\\ =\sqrt{94236827.78}\\ =9707.57\end{array}$

Standard deviation is $303.35 and mean is $9707.7 therefore the policy on an arbitrary Choose varies $303.35 from the mean $9707.7