Overbooking flights

Eagle Air is a small commuter airline.  Eachof their planes holds 15 people. Past records indicatethat only 80% of people with reservations (tickets) do showup. Therefore, Eagle Air decides to overbook every flight.Suppose Eagle Air decides that it will accept up to 18 reservationsper flight (18 is the maximum number of reservations perflight).

Demand for Eagle Air flights is so strong that 18reservations are booked for every flight. Everyone knowshow popular Eagle Air flights are, and so no one ever shows upwithout a reservation.

This is the first of 6 questions in thisset.

a. Calculate the probability that on any given flight, at leastone passenger holding a reservation will not have aseat.  Four decimals

b. What is the probability that there will beone or more empty seats? Four decimals

c. What is the probability that the firstperson who is bumped from a flight will not get on either of thenext two flights? Assume that the number of “no-shows” isindependent across flights. Also assume that the first person whois bumped has priority when an empty seat comes up on a subsequentflight.  Four decimals

d. What is the expected number of people whoshow up for a flight? Reminder: Everyone makes a reservation ahead;no one shows up without a reservation; a maximum of 18 reservationsis accepted; and every flight has 18 reservations because Eagle Airis so popular.  One decimal

e. Suppose that each flight costs $1000 to run,considering all costs. If tickets are priced at $75 each, what isEagle Air’s expected profit per flight? Assume that when sixteen ormore people show up for a flight, any overbooked passengers waituntil a seat becomes available, so Eagle Air ultimately gets therevenue from everyone who shows up.  Onedecimal

f. What is the standard deviation of the numberof people who show up for a flight? Twodecimals