A tire manufacturer believes the tread life of its snow tires can be described by a normal distribution with a mean of 32,000 miles and a standard deviation of 7000 miles. Find the probability (rounding to tenth of percent) that a randomly selected tire will have a tread life:

a. of at least 40,000 miles b. of 30,000 or less miles

c. that last between 30,000 and 35,000 miles

d. In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer doesn't want to take too big a financial risk with this guarantee. If the dealer is willing to give refunds to no more than 1 out of every 50 tires sold, for what mileage can he guarantee each tire to last ?

(Round to the nearest whole number)

e. Find the probability that 50 randomly chosen tires will have a mean tread wear of greater than 35,000 miles ? (Round to tenth of a percent)

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