The number of no-shows is normally distributed

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Nittany Lion Inn (NLI) experiences a high influx of demand during the football season. Interestingly, there are quite a few no-shows for all the bookings made. To ensure that rooms do not go unsold during the primes season, resorts to overbooking. Rooms are booked for $200 a night. The number of no-shows is normally distributed with a mean of 50 and standard deviation of 15. If a customer with booking cannot be given a room, NLI reimburses them with cash equal to 50% of what they paid for their room, and makes arrangement for them to be housed in nearby hotel (XYZ) at no cost to them; XYZ however, charges NLI $150 per room. Optimally how many over bookings should NLI do?

Reference no: EM1389691

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