A brake pad manufacturer claims its brake pads will last for

A brake pad manufacturer claims its brake pads will last for 38,000 miles. You work for a consumer protection agency and you are testing this manufacturer\'s brake pads. Assume the life spans of the brake pads are normally distributed. You randomly select 50 brake pads. In your tests, the mean life of the brake pads is 37,650 miles. Assume sigma =1000 miles

(a) Assuming the manufacturer\'s claim is correct. What is the probability that the mean of the sample is 37,650 miles or less?

(b)Using your answer from part (a), what do you think of the manufacturer\'s claim?

(c) Would it be unusual to have an individual brake pad last for 37,650? Why or why not?

Solution

(a) The probability is

P(xbar<37650) = P((xbar-mean)/(s/vn) <(37650-38000)/(1000/sqrt(50)))

=P(Z<-2.47) = 0.0068 (from standard normal table)

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(b) Since the probability is less than 0.05, the manufacturer\'s claim is not correct.

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(c) No, it would be unusual to have an individual brake pad last for 37,650 because the probabilty is less than 0.05