A national tire manufacturer Machelin has a popular all season treaded tire mean

Question

A national tire manufacturer Machelin has a popular all season treaded tire meant for use on light trucks and SUVs and according to the company, the average tread wear for this tire should be 63 thousand miles. 40 tires (10 Cars) were randomly selected and driven until they were in need of replacement. The results of the test were a mean tread wear of 61.2 thousand miles with a standard deviation of 1.8 thousand miles. Historically the true tread wear of ALL tires for Machelin vary by 1.57 thousand miles. Construct a 99% interval estimate to determine if the tires wear out too fast.

Explanation / Answer

mean = 61.2 SD = 1.8

sample = 40

alpha / 2 = 0.005 Z= 2.57

I: 61.2 +/- 2.57 * 1.8 / srqt 40

61.2 +/- 0.7314

60.4686 < miu < 61.9314

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