A tire manufacturer believes that the tread life of its snow tires can be described by a

Question:

A tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with a mean of 32,000 miles and a standard deviation of 2500 miles.
a) If you buy a set of these tires, would it be reasonable for you to hope that they’ll last 40,000 miles? Explain.
b) Approximately what fraction of these tires can be expected to last less than 30,000 miles?
c) Approximately what fraction of these tires can be expected to last between 30,000 and 35,000 miles?
d) Estimate the IQR for these data.
e) In planning a marketing strategy, a local tire wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the does not want to take too big a risk. If the is willing to give refunds to no more than 1 of every 25 customers, for what mileage can he guarantee these tires to last?
Dealer
A dealer in the securities market is an individual or firm who stands ready and willing to buy a security for its own account (at its bid price) or sell from its own account (at its ask price). A dealer seeks to profit from the spread between the...