A certain brand of automobile tire has a mean life span of 36,000 miles and a st

Question

A certain brand of automobile tire has a mean life span of 36,000 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 35,000 miles, 37,000 miles, and 31,000 miles. Find the z-score that corresponds to each life span. For the life span of 35,000 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 31,000 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 " Yes (b) The life spans of three randomly selected tires are 33,600 miles, 38,400 miles, and 36,000 miles. Using the empirical rule, find the percentile that corresponds to each life The life span 33,600 miles corresponds to the th percentile The life span 38,400 miles corresponds to the th percentile The life span 36,000 miles corresponds to the percentile Click to select your answer(s) 0 Type here to search

Explanation / Answer

as z score =(X-mean)/std deviaiton

a)..35000 miles; z score is =(35000-36000)/2400=-0.42

,,37000 miles; z score is =(37000-36000)/2400=0.42

..31000 miles; z score is =(31000-36000)/2400=-2.08

Yes

b)

33600 miles coresponds to 16th percentile

38400 miles coresponds to 84th percentile

36000  miles coresponds to 50th percentile

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