Suppose that the balance on Sears's charge cards last month is a normally distributed random variable with mean $50 and standard deviation $8.

(a) Find the probability that a randomly chosen charge card will have a balance of at least $40.

(b) Find the probability that a randomly chosen charge card will have a balance of less than $42.

(c) If a random sample of 64 charge cards is selected, find the probability that the average balance is less $51.

(d) 2.5% of the charge cards will have balances above what value?