Chapter 16, Problem 33E

(a)

To determine

To Calculate: the mean and standard deviation.

Answer to Problem 33E

Mean = 23.4

Standard deviation = 12.6

Explanation of Solution

Given:

  $\begin{array}{c}E\left(X\right)=1.3\\ SD\left(X\right)=0.7\end{array}$

Formula used:

  $\begin{array}{l}E\left(X\right)={\displaystyle \sum xP\left(X=x\right)}\\ \text{Var}\left(X\right)={\displaystyle \sum {(x-\mu )}^{2}P\left(x\right)}\\ SD\left(X\right)=\sqrt{\mathrm{var}\left(X\right)}\end{array}$

Calculation:

Suppose that

X is the number of parking tickets that the truck would get this month.

Y is the number of parking tickets that 18 trucks would get month.

  $Y=18X$

Compute the mean and standard deviation.

Mean:

  $\begin{array}{c}E\left(Y\right)=E\left(18X\right)\\ =18E\left(X\right)\\ =18{\left(1.3\right)}^2\\ =23.4\end{array}$

Variance:

  $\begin{array}{c}\mathrm{var}\left(Y\right)=\mathrm{var}\left(18X\right)\\ ={18}^2\mathrm{var}\left(X\right)\\ ={18}^2{\left(0.7\right)}^2\\ ={18}^2\left(0.49\right)\end{array}$

Standard deviation:

  $\begin{array}{c}SD\left(Y\right)=\sqrt{\mathrm{var}\left(Y\right)}\\ =\sqrt{{18}^2{\left(0.7\right)}^2}\\ =18\times 0.7\\ =12.6\end{array}$

Therefore, the mean is 23.4 and SD is 12.6

(b)

To determine

To Explain: the assumption that make in answering.

Explanation of Solution

The parking tickets that a truck get is not dependent of parking tickets that another truck gets.