Chapter 6, Problem 17E

a)

To determine

To explain how many standard deviations from the mean would a steer weighing 1000 pounds.

Answer to Problem 17E

The steer weighing 1000 pounds is 1.81 standard deviations below the mean.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $z=\frac{x-\mu }{\sigma }$

  $z=\frac{1000-1152}{84}=-1.81$

Therefore, the steer weighing 1000 pounds is 1.81 standard deviations below the mean.

b)

To determine

To explain which one is more unusual.

Answer to Problem 17E

The most unusual value is that value which is furthest from 0 and so, the steer weighing 100 pounds is the most unusual.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

Formula:

  $z=\frac{x-\mu }{\sigma }$

For $x$ = 1000

  $z=\frac{1000-1152}{84}=-1.81$

For $x$ = 1250

  $z=\frac{1250-1152}{84}=1.17$

Therefore, the most unusual value is that value which is furthest from 0 and so, the steer weighing 100 pounds is the most unusual.