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(Solved): 2. (4 pts) A particular brand of tires has a mean lifetime of 62,000 miles with a standard ...
2. (4 pts) A particular brand of tires has a mean lifetime of 62,000 miles with a standard deviation o 1,500 miles. Assume the lifetime of a tire is normally distributed. a) What is the probability that a randomly selected tire of this brand lasts between 65,000 and 70,000 miles? b) What is the probability that a randomly selected tire of this brand lasts more than 64,000 miles? c) Is a tire lifetime of 64,000 miles unusually high for a randomly selected tire of this brand? Wh or why not? d) What lifetime do \( 40 \% \) of all tires of this brand have less than?
Expert Answer
x be the lifetime of tires. x follows normal distribution with mean ( µ ) = 62000 and standard deviation (?) = 1500 a) P( 65000 ? x ? 70000 ) =P( x ? 70000 ) - P( x ? 65000 ) For x = 70000 z = z = 5.33 Area corresponding to 5.33 on z score table is a