Normal or not does it matter A manufacturer of automobile b

Normal or not - does it matter?

A manufacturer of automobile batteries claims that the

length of life for their batteries is normally distributed with a mean of 60 months and a standard

deviation of 10 months (i.e. battery life

N

(60

;

10

2

)).

(a) Describe the sampling distribution of the sample mean for samples of size 16, i.e. describe

the distribution of the average life time of these automobile batteries for samples of size

16.

i. shape:

Normal

Not Normal

Not enough information to tell

ii. mean:

(Report to the nearest two decimal places.)

iii. standard error:

(Report to the nearest two decimal places.)

(b) How would your answer in part (a) change if the battery life did not follow a normal

distribution?

i. only the mean changes

ii. only the standard error changes

iii. both the mean and standard error change

iv. only the shape changes

v. the mean, standard error, and shape change

vi. none of these change

vii. not enough information to tell

(c) How would your answer in part (a) change if the battery life did not follow a normal

distribution and the sample size was 45 instead of 16?

i. only the mean changes

ii. only the standard error changes

iii. both the mean and standard error change

iv. only the shape changes

v. the mean, standard error, and shape change

vi. none of these change

vii. not enough information to tell

Solution

a) i) Normal ii) mean=60 ,iii)standard deviation=2.5

b) ii)

c) ii)