5. At a local hardware store, the demand, per week, for propane gas, primarily for barbecue propane tanks, in 100’s of gallons, is a randomvariable with probability density function

(a) How many gallons of propane gas must the hardware store carry, per week, so that the stock out probability for the gas is at most 0.05?

(b) Suppose that on a Sunday morning, when the store opens, it has 590 gallons of propane gas. What is the expected value of its inventory of gas on the following Saturday evening when the store closes, given that no propane gas delivery has been made all week?

f(x) = 0 75 (6-22) 2 1x6 otherwise.