Chapter 6, Problem 18E

a)

To determine

To explain how many standard deviations from the mean would a car going under the speed limit.

Answer to Problem 18E

The car going under the speed limit is more than 1.08 standard deviations below the mean.

Explanation of Solution

Given:

Speed limit = $x$ = 20

  $\mu$ = 23.48

  $\sigma$ = 3.56

Formula:

  $z=\frac{x-\mu }{\sigma }$

  $z=\frac{20-23.84}{3.56}=-1.08$

Therefore, the car going under the speed limit is more than 1.08 standard deviations below the mean.

b)

To determine

To explain which one is more unusual.

Answer to Problem 18E

The car travelling at 10 mph is the most unusual.

Explanation of Solution

Given:

  $\mu$ = 23.48

  $\sigma$ = 3.56

Formula:

  $z=\frac{x-\mu }{\sigma }$

Speed limit = $x$ = 10

  $z=\frac{10-23.84}{3.56}=-3.89$

Speed limit = $x$ = 34

  $z=\frac{34-23.84}{3.56}=2.85$

Therefore, the most unusual values having a z-score furthest from 0. Hence, car travelling at 10 mph is the most unusual.