The useful life of a particular make and type of automotive tire is normally dis

Question

The useful life of a particular make and type of automotive tire is normally distributed with mean 57,500 miles and standard deviation 950 miles.

a. Find the probability that such a tire will have a useful life of between 57,000 and 58,000 miles.

b. Hamlet buys four such tires. Assuming that their lifetimes are independent, find the probability that all four will last between 57,000 and 58,000 miles. (If so, the best tire will have no more than 1,000 miles left on it when the first tire fails.) Hint: There is a binomial random variable here, whose value of p comes from part (a).

Explanation / Answer

Mean=57,500 miles

Standard Dev=950 miles

A. P(between 57000 and 58000)

Using normal distribuiton table, P(A)=0.4013

use this link http://onlinestatbook.com/2/calculators/normal_dist.html

B. Since they are independent events

P(all four between 57000 and 58000 miles)=0.4013^4=0.02593

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