5.27 A contractor has concluded from his experience that the cost of building a luxury home is a normally distributed random variable with a mean of $500,000 and a standard deviation of $50,000.

a. What is the probability that the cost of building a home will be between $460,000 and $540,000?

b. The probability is 0.2 that the cost of building will be less than what amount?

c. Find the shortest range such that the probability is 0.95 that the cost of a luxury home will fall in this range.