Question

A brake pad manufacturer claims that the mean life of its brake pads will last for 38,000 miles with
standard deviation=1000 miles. You work for a consumer protection agency and you are testing this
manufacturer’s brake pads. Assume that the life spans of the brake pads are normally distributed.
(a) You examined an individual brake pad and it lasts for 37,650 miles. Calculate the probability
of having an individual brake pad that lasts for 37,650 miles. Assume the manufacturer’s
claim is correct.
(b) You randomly select 50 brake pads for checking, the mean life of the brake pads is 37,650
miles. State the type of distribution used to model the mean life of the brake pads and give a
brief explanation. In addition, sketch the shape of the distribution with the specification of its
mean and standard deviation.
(c) Assuming the manufacturer’s claim is correct, calculate the probability that the mean of the
sample is 37,650 miles or less.
(d) Using your answer from part (c), do you believe that the manufacturer’s claim is correct?
State your viewpoint with a supporting reason.
(e) Suggested a probability distribution for modelling the sample mean under the following
situations:
 Sample size = 10, the population is normally distributed
 Sample size = 10, the population is not normally distributed
 Sample size = 100, the population is normally distributed
 Sample size = 100, the population is not normally distributed

Answer 1

The life of brake pads is normally distributed .

a) The probability of having an individual brake pad that lasts for 37,650 miles is

b) The distribution of the mean is normal accordingto CLT. Here .

The distribution is sketched below.

c) The probability that the mean of the sample is 37,650 miles or less

d) The probability that the life of brake pads is less than 37,650 miles is very less. So the manufactures claim might be right.

e) According to CLT (Central Limit Theorem), the mean is approximately normally distributed. So in each case, the distribution is normal