A tire manufacturer offers a warranty that the set of (four) tires it sells last a minimum of 20,000 miles. If a single tire in that set fails before 20,000 miles, a (complete) set is replaced at no additional cost to the customer.

From its past experience, the manufacturer estimates that a set of tires lasts on average 26,000 miles, with a SD of 5,000 miles and a normal distribution. Not counting the cost of replacement, the manufacturer's profit on each sold set is $200. If the manufacturer ends up replacing a set of tires, he incurs a cost of $400, netting a loss of $200 on that transaction.

1. What is the probability that a set of tires wears out before 20,000 miles?
2. What is the probability that the manufacturer turns a profit on selling one set?
3. What is expected profit on one set of tires?

Suppose the manufacturer sells 900 sets. The buyers' driving experiences and the wear tear on those sets are assumed to be independent from each other.Is the manufacturer more likely or less likely to make a loss from selling the 900 sets compared to selling a single set?

1. [Hint: treat the 900 sets as independent samples from the population (of sets of tires). What does averaging over 900 sets do to variability?]