Chapter 6, Problem 20E

a)

To determine

To find the mean and standard deviation.

Answer to Problem 20E

New mean is 3.84 mph and standard deviation is 3.56 mph.

Explanation of Solution

Given:

  $\mu$ = 23.48

  $\sigma$ = 3.56

All the values decreased by 20 mph. Therefore, the mean is also decreased by 20 mph.

Then the new mean is,

  $\mu ={\mu }_{old}-20=23.84-20=3.84mph$

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

Therefore, $\sigma ={\sigma }_{old}=3.56mph$

b)

To determine

To find the mean and standard deviation.

Answer to Problem 20E

New mean is 38.3586 km/h and standard deviation is 5.72804 km/h.

Explanation of Solution

Given:

  $\mu$ = 23.48

  $\sigma$ = 3.56

All the values multiplied by 1.609.

Then the new mean is,

  $\mu =1.609\times {\mu }_{old}=1.609\times 23.84=38.35856km/h$

Therefore, $\sigma =1.609\times {\sigma }_{old}=1.609\times 3.56=5.72804km/h$