Chapter 13.2, Problem 64E

a.

To determine

The higher probability out of choosing a car at random that has a fuel efficiency of $26-28$ mpg or one with fuel efficiency of $22-24$ mpg.

Answer to Problem 64E

Probability to get a car having fuel efficiency between $26-28$ mpg is greater.

Explanation of Solution

Given Information: A bell shaped curve is given.

Calculation:

  $26-28$ mpg corresponds to $\sigma >x>\overline{x}$ which represents $34.1\%$ of the total area of the curve.

Probability ( $26-28$ mpg) $=0.341$

Whereas $22-24$ mpg corresponds to $-2\sigma <x<-\sigma$ which represents $13.6\%$ of the total area of the curve.

Probability ( $22-24$ mpg) $=0.136$

Thus, probability to get a car having fuel efficiency between $26-28$ mpg is greater.

b.

To determine

The higher probability out of choosing a car at random that has a fuel efficiency of $20-22$ mpg or one with fuel efficiency of at least $30$ mpg.

Answer to Problem 64E

Probability to get a car having fuel efficiency between of at least $30mpg$ is greater.

Explanation of Solution

Given Information: A bell shaped curve is given.

Calculation:

  $20-22$ mpg corresponds to $-3\sigma <x<-2\sigma$ which represents $2.1\%$ of the total area of the curve.

Probability ( $20-22$ mpg) $=0.021$

Greater than $30$ mpg corresponds to $2\sigma <x<4\sigma$ which represents $2.14\%$ and $0.13\%$ of the total area of the curve.

Probability $=0.021+0.0013$

  $=0.0223$

Thus, probability to get a car having fuel efficiency between of at least $30mpg$ is greater.