Normal or not - does it matter? A manufacturer of automobile batteries claims th
ID: 3381411 • Letter: N
Question
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
Explanation / Answer
a) i) Normal ii) mean=60 ,iii)standard deviation=2.5
b) ii)
c) ii)
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