Chapter 10.3, Problem 17E

To determine

To calculate:

The quickest route to use

Answer to Problem 17E

The route $B$ has the best probability of getting to school on the time.

Explanation of Solution

Given information:

  

Calculation:

This question deals with study of two way table with provided the values of experiment is being considered.

	On time	Late	Total
Route $A$	$7$	$4$	$11$
Route $B$	$11$	$3$	$14$
Route $C$	$12$	$4$	$16$
Route $D$	$30$	$11$	$41$

Use findings to make the two ways table shows the marginal relative frequencies and the joint. There are total $41$ observations in this table.

		Result
		On Time	Late	Total
Route	$A$	$0.171$	$0.098$	$0.268$
	$B$	$0.268$	$0.073$	$0.342$
	$C$	$0.293$	$0.098$	$0.39$
	Total	$0.732$	$0.268$	$1$

The conditional probabilities by dividing the joint relative frequency in the column “on the time” by the marginal relative frequency in its row:

Probability of on time for route $A$

  $\begin{array}{l}P\left(ontime/RouteA\right)=\frac{P\left(RouteAandontime\right)}{P\left(RouteA\right)}\\ P\left(ontime/RouteA\right)=\frac{0.171}{0.268}\\ P\left(ontime/RouteA\right)=0.638\end{array}$

Probability of on time for route $B$

  $\begin{array}{l}P\left(ontime/RouteB\right)=\frac{P\left(RouteBandontime\right)}{P\left(RouteB\right)}\\ P\left(ontime/RouteB\right)=\frac{0.268}{0.342}\\ P\left(ontime/RouteB\right)=0.784\end{array}$

Probability of on time for route $C$

  $\begin{array}{l}P\left(ontime/RouteC\right)=\frac{P\left(RouteCandontime\right)}{P\left(RouteC\right)}\\ P\left(ontime/RouteC\right)=\frac{0.268}{0.342}\\ P\left(ontime/RouteC\right)=0.784\end{array}$

As per the observation, the route $B$ has the best probability of getting to school on the time.