The phone lines to airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 100 calls are placed to the airline. Let Y be the number of calls that are occupied.
a) Verify that Y follows a binomial distribution. (Check the four assumptions of binomial distribution)
b) What is the probability that the lines are occupied for exactly 20 calls.
c) What is the probability that the lines are occupied for at least 20 calls.
d) What is the probablity that the lines are occupied for at least 20 calls and at most 80 calls.
e) Calculate the expected number of calls that are occupied.
f) Calculate the variability of the number of calls that are occupied.