Chapter 6.2, Problem 40E

(a)

To determine

To Construct: a graph of the probability and explain its shape

Explanation of Solution

Given:

Total Garage fee (Y)	$10	$13	$15	$20
Probability P(y)	0.20	0.25	0.45	0.10

Y= garage fee

Calculation:

$3 required to paid additional to the garage fee so the total amount is increased by $3

X=Y+3

Garage fee (Y)	$13	$16	$18	$23
Probability P(y)	0.20	0.25	0.45	0.10

Graph:

  

The distribution is not symmetric, highest bars in the middle at X=18 which is single peak and has the highest probability and lowest bars is at the end at X=23 which has the lowest probability.

(b)

To determine

To Calculate: the ${\mu }_T$ and explain it

Answer to Problem 40E

  ${\mu }_T=17$

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_G=14\\ {\sigma }_G=2.74\end{array}$

Calculation:

Y= garage fee $3 required to paid additional to the garage fee so the total amount is increased by $3

X=Y+3

Adding the constant to every data value, then the center of the distribution is also increased by that constant value

  $\begin{array}{c}{\mu }_T={\mu }_G+3\\ =14+3\\ =17\end{array}$

If adding the constant value to every data it will increase ( ${\mu }_G+3$ ) the center of the distribution here the total amount is increased by $3, so $17 average money will be randomly selected.

(c)

To determine

To Calculate: the ${\sigma }_T$ and explain it

Answer to Problem 40E

  ${\sigma }_T=2.74$

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_G=14\\ {\sigma }_G=2.74\end{array}$

Calculation:

Y= garage fee $3 required to paid additional to the garage fee so the total amount is increased by $3

X=Y+3

Adding the constant to every data value, then the spread of the distribution will not affect, it remains unchanged.

  ${\sigma }_X={\sigma }_Y=2.74$

If adding the constant value to every data, then it will not affect the spread of the distribution so money for a arbitrary selected varies on average $2.74 about the mean =$17