Question

Two companies market new batteries targeted at owners of personal music players. Brand A claims a mean battery life of

1111

​hours, while Brand B advertises

1313

hours. Complete parts a through c below.

​a) Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to buy.

A.

The standard deviation can be used to determine which battery is more reliable.

B.

The standard deviation can be used to determine whether the mean battery life is valid.

C.

The standard deviation can be used to determine exactly how long a battery will last.

D.

The standard deviation can be used to determine the likelihood that a brand of battery will last a certain amount of time.

Answer 1

Answer

we have the mean value for each battery. We know that the formula for z is given as

$z = (\bar{x}-\mu)/\sigma$

So, if we know the standard deviation then we can determine the likelihood that a brand of battery will last a certain amount of time.

For example, if we have standard deviation = 2 for Brand A and we want to determine the probability that it will last 14 hours

then we can solve the following equation

$z = (\bar{x}-\mu)/\sigma$ = (14-11)/2 = 3/2 = 1.5

Then using z distribution to find the corresponding p value for the likelihood.

So, option D is correct answer