A manufacturer claims that the life span of its tires is 53,000 miles. You work
ID: 3268283 • Letter: A
Question
A manufacturer claims that the life span of its tires is 53,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 52,849 miles. Assume =700.
Complete parts (a) through (c).
(a) Assuming the manufacturer's claim is correct, what is the probability that the mean of the sample is
52,849 miles or less?
(Round to four decimal places as needed.)
(b) Using your answer from part (a), what do you think of the manufacturer's claim?
The claim is inaccurate/accurate because the sample mean would/would not be considered unusual since it lies/does not lie within the range of a usual event, namely within 1 standard deviation/2 standard deviation/3 standard deviation of the mean of the sample means.
(c) Assuming the manufacturer's claim is true, would it be unusual to have an individual tire with a life span of 52,849 miles? Why or why not?
Yes/No, because 52,849 lies/does not lie within the range of a usual event, namely within 1 standard deviation/2 standard deviation/3 standard deviation of the mean for an individual tire.
Explanation / Answer
a)
P(X < 52849)
= P(Z < 52849 - 53000/700/sqrt(100))
= P(Z < -2.157)
= 0.0155
b)
the claim is accurate because the sample mean would not be considered unusual since it lie within the range of a usual event namely within 1 standard deviation of the mean of sample means
c)
No, because 52,849 lie within the range of a usual event, namely within 1 standard deviation of the mean for an individual tire.
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