A certain brand of automobile tire has a mean life span of 38,000 miles and a st

Question

A certain brand of automobile tire has a mean life span of 38,000 miles and a standard deviation of 2,400 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 33,000 miles, 37,000 miles, and 32,000 miles. Find the z-score that corresponds to each life span. For the life span of 33,000 miles, z-score is (Round to the nearest hundredth as needed.) For the life span of 37,000 miles, z-score is (Round to the nearest hundredth as needed.) For the life span of 32,000 miles, z-score is (Round to the nearest hundredth as needed.) According to the z-scores, would the life spans of any of these tires be considered unusual? O No O Yes (b) The life spans of three randomly selected tires are 33,200 miles, 42,800 miles, and 38,000 miles. Using the empirical rule, find the percentile that corresponds to each life span The life span 33,200 miles corresponds to the th percentile. The life span 42,800 miles corresponds to theth percentile The life span 38,000 miles corresponds to the th percentile.

Explanation / Answer

Z= (33000-38000)/2400=-2.0833 Percentile=0.018612=1.86%

Z=(37000-38000)/2400=-0.41667 Percentile=33.846%

Z= (32000-38000)/2400=-2.5 Percentile=0.621%

2) Z scores of tyre with 32000 and 33000 are more than 2. Hence, these are unusual.

3)

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