Chapter 6.2, Problem 41E

(a)

To determine

To Explain: the shape of the distribution

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_X=3.87\\ {\sigma }_X=1.29\end{array}$

Cost of ferry trip = $5

X is representing the number of cars which is arbitrary selected where M representing the money collected on a randomly selected ferry trip.

Ferry trip per car cost is $5 so the money gained on the ferry trip is then the product of the number of cars and the cost of the ferry trip every car

  $M=5\times X$

If every certain value is multiplied by the same constant, then the shape of the distribution will not affect.

The distribution is skewed to the left, because the lowest bar is to the left in the given histogram and the highest bar is to the right in the given histogram. The distribution of M then has the same shape as the distribution of X, skewed to the left

I

(b)

To determine

To Calculate: the mean of M

Answer to Problem 41E

  $M=19.35$

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_X=3.87\\ {\sigma }_X=1.29\end{array}$

Calculation:

  $\begin{array}{c}M=5\times {\mu }_X\\ =5\times 3.87\\ =19.35\end{array}$

X is representing the number of cars which is arbitrary selected where M representing the money collected on a randomly selected ferry trip.

Ferry trip per car cost is $5 so the money gained on the ferry trip is then the product of the number of cars and the cost of the ferry trip every car

  $M=5\times X$

If every certain value is multiplied by the same constant, then the center of the distribution is also multiplied by the same constant so the mean of M will be multiplied by 5. Average $19.35 money will be collected from an arbitrary selection.

(c)

To determine

To Calculate: the standard deviation of M

Answer to Problem 41E

  ${\sigma }_M=6.45$

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_X=3.87\\ {\sigma }_X=1.29\end{array}$

Calculation:

  $\begin{array}{c}{\sigma }_M=5\times {\sigma }_X\\ =5\times 1.29\\ =6.45\end{array}$

X is representing the number of cars which is arbitrary selected where M representing the money collected on a randomly selected ferry trip.

Ferry trip per car cost is $5 so the money gained on the ferry trip is then the product of the number of cars and the cost of the ferry trip every car

  $M=5\times X$

Multiplying every certain value by the same constant, then the spread of the distribution is affected in the same way so the standard deviation will be multiplied by 5. Money gained on a randomly selected ferry trip varies on average by $6.45 from the mean amount $19.35