Problem $4.$ An airline has found that the number of people who purchased tickets and did not show up for

a flight is normally distributed with mean of $20$ and standard deviation of $10.$ The airline estimates that

the ill will and penalty costs associated with not being able to board a passenger holding confirmed

booking are estimated to be $$600.$ Assume that the opportunity cost of flying an empty seat is $$100($price

that a passenger who shows up$,$ would pay$).$ There are $225$ seats on the plane. How much should airline

overbook the flight $(b^{**}-C)?$