Airlines and hotels often grant reservations in excess of ca

Airlines and hotels often grant reservations in excess of capacity to minimize losses due to no-shows. Suppose the records of a hotel show that, on the average, 10% of their prospective guests will not claim their reservation. If the hotel accepts 331 reservations and there are only 300 rooms in the hotel, what is the probability that all guests who arrive to claim a room will receive one? (Round your answer to four decimal places.)

Solution

expected number of people arrive =np=331*0.9=297.9

std deviation =(np(1-p))^1/2 =5.458

hence from normal approximation and continuity correction:

probability that all guests who arrive to claim a room will receive one:

P(X<=300)=P(Z<(300.5-297.9)/5.458)=P(Z<0.48)=0.6844