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 289 reservations and there are only 260 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

hre mean number of cumstomer who claim reservation =np =289*0.9=260.1

and std deviaiton =sqrt(np(1-p)) =4.614

as we know that for normal distribution z score =(X-mean)/std deviation

hence from normal approximation and with continuity correction;  probability that all guests who arrive to claim a room will receive one :