A manufacturer claims that the life span of its tires is 52,000 miles. You work

Question

A manufacturer claims that the life span of its tires is 52,000 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 51,828 miles. Assume =900. Complete parts (a) through (c). (a) Assuming the manufacturer's claim is correct, what is the probability that the mean of the sample is 51,828 miles or less? nothing (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 not would be considered unusual since it does not lie lies within the range of a usual event, namely within 1 standard deviation 2 standard deviations 3 standard deviations 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 51,828 miles? Why or why not? No Yes , because 51,828 lies does not lie within the range of a usual event, namely within 1 standard deviation 2 standard deviations 3 standard deviations of the mean for an individual tire.

Explanation / Answer

a)
P(X < 51828)
= P(z < (51828 - 52000)/(900/sqrt(100)))
= P(z < -1.9111)
= 0.0280

b)
the claim is inaccurate because the sample mean would be considered unusual since it does not lies within the range of a usual event namely within 1 standard deviationof the mena of the sample means.

c)
P(X < 51828)
= P(z < (51828 - 52000)/(900/sqrt(1)))
= P(z < -0.1911)
= 0.4242

No, because 51828 lies within the range of usual event, namely within 1 sd of the mean for an individual tire

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