An importer of shirts made in China buys the shirts in lots of 100 from a supplier who guarantees that no more than 2% of the shirts are faulty. On a given day, 15 lots are delivered to the importer.

(a) What is the probability that, in a given lot of 100 shirts, more than 5 shirts are faulty?

(b) What is the expected number of faulty shirts in a lot selected at random?

(c) A lot is rejected if it has more than 4 faulty shirts. What is the probability that a lot is rejected?

(d) What is the probability that more than 3 lots out of the 15 are rejected?

(e) On average, how many lots out of the 15 will be rejected?