Chapter 7, Problem AP2.20CPT

To determine

To find: the following are the mean and standard deviation, respectively, of the winnings.

Answer to Problem AP2.20CPT

$15.00, $53.85

Explanation of Solution

Given:

  

Formula used:

  $\begin{array}{l}\mu ={\displaystyle \sum x}\times p\left(x\right)\\ {\sigma }^2={\displaystyle \sum {\left(x-\mu \right)}^2}\times p\left(x\right)\\ \sigma =\sqrt{{\sigma }^2}\end{array}$

Calculation:

  $\mu =500\times 0.01+100\times 0.05+25\times 0.20+0\times 0.74=15$

Variance

  $\begin{array}{c}{\sigma }^2={\left(500-15\right)}^2\times 0.01+{\left(100-15\right)}^2\times 0.05\\ +{\left(25-15\right)}^2\times 0.20+{\left(0-15\right)}^2\times 0.74\\ =2900\end{array}$

Standard deviation

  $\sigma =\sqrt{2900}=53.85$

Hence, the correct option is (b)