Tirerack guarantees that the maximum life span for a set of tires is 20,000 mile

Question

Tirerack guarantees that the maximum life span for a set of tires is 20,000 miles It also guarantees that any customer who has to replace their tires at 15,000 miles or less will receive a 50% discount on a new set of tires. It is estimated that the mean life of these tires is 25,000 with the standard deviation is 2400 minutes. Suppose the lifespan of these tires is normally distributed. What proportion of customers would you expect will receive a 50% discount on their next set of tires? (Round your answer to the nearest thousandth.)   

What influences would you predict that would cause the real incidence of this discount to be lower/higher than predicted?

Explanation / Answer

Suppose the lifespan of these tires is normally distributed. What proportion of customers would you expect will receive a 50% discount on their next set of tires?

Proportion of customers is P( z < [ 15000 - 25000 ] / 2400)

P( z < -4.17) = 0.00005

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