Chapter 6, Problem 19E

a)

To determine

To find the mean and standard deviation of the sale prices for all the steers.

Answer to Problem 19E

New mean is 152 and standard deviation is 84.

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

All the values decreased by 1000 pounds. Therefore, the mean is also decreased by 1000 pounds.

Then the new mean is,

  $\mu ={\mu }_{old}-1000=1152-1000=152$

There will be no impact on standard deviation because the spread of the data values will not change by adding subtracting any value.

Therefore, $\sigma ={\sigma }_{old}=84$

b)

To determine

To find the mean and standard deviation of the sale prices for all the steers.

Answer to Problem 19E

New mean is $460.80 and standard deviation is $33.60

Explanation of Solution

Given:

  $\mu$ = 1152

  $\sigma$ = 84

All the values multiplied by $0.4.

Then the new mean is,

  $\mu =0.4\times {\mu }_{old}=0.4\times 1152=\$460.80$

Therefore, $\sigma =0.4\times {\sigma }_{old}=0.4\times 84=\$33.60$