A contractor regards the cost of fulfilling a particular contract as a normally distributed random variable with mean $500,000 and standard deviation $50,000.

(a) What is the probability that the cost of fulfilling the contract will be between $460,000 and $540,000?

(b) The probability is .2 that the contract will cost less than how much to fulfill?

(c) Find the shortest range such that the probability is 95 that the cost of fulfilling the contract will fall in this range.