Chapter 6, Problem 16E

a)

To determine

To explain why standard deviations is useful.

Explanation of Solution

Given:

Mean battery life = $\mu$ = 11

MeanRockReady advertises = $\mu$ = 12

The standard deviation that reported with mean will given a better reflection of battery life. Therefore, z-score can be found and used to determine the best battery life.

b)

To determine

To explain which battery is most likely to last all day.

Answer to Problem 16E

DuraTunes has the higher z value and the longer battery life over 8 hours.

Explanation of Solution

Given:

Mean battery life = $\mu$ = 11

Mean RockReady advertises = $\mu$ = 12

Formula:

  $z=\frac{x-\mu }{\sigma }$

DuraTunes:

  $z=\frac{8-11}{2}=-1.5$

RockReady:

  $z=\frac{8-12}{1.5}=-2.7$

Therefore, DuraTunes has the higher z value and the longer battery life over 8 hours.

b)

To determine

To explain which battery is most likely to last all day.

Answer to Problem 16E

RockReady has the higher z value and the longer battery life over 16 hours.

Explanation of Solution

Given:

Mean battery life = $\mu$ = 11

Mean RockReady advertises = $\mu$ = 12

Formula:

  $z=\frac{x-\mu }{\sigma }$

DuraTunes:

  $z=\frac{16-11}{2}=2.5$

RockReady:

  $z=\frac{16-12}{1.5}=2.7$

Therefore, RockReadyhas the higher z value and the longer battery life over 16 hours.