During high season, it is common that hotels take on more bookings than the number of rooms they have. The reason being that bookings are often cancelled last

minute. However, it can happen that everyone shows up and then there are not enough rooms available. This overbooking situation can be costly for the hotel as

they need to send their possibly unhappy guests to another hotel. Land Hotel is a new hotel close to Turkey's main shopping street. It has 196

rooms. The hotel is very busy on a particular weekend in the end of August when Turkey's Cultural Day takes place with Turkey Marathon and numerous other

events going on. However, in the past Land hotel has had some guests cancelling last minute.

Land Hotel is interested in understanding the implication of taking on more bookings than there are rooms. They estimate the cancelling probability on this weekend to

be 5%. The socalled binomial distribution can be used to describe uncertain situations of this kind where there are two possible outcomes; a guest shows up or

not. Fortunately, the binomial distribution can be approximated by the normal distribution such that the number of guests that show up is normally

distributed with a mean of np and a standard deviation of n p ( 1 p) where n is the number of rooms booked and p is the probability of showing up.

a) If the hotel books 205 rooms on the Cultural Day what is the probability that there will be an overbooking situation?

b) If the hotel books 210 rooms on the Cultural Day what is the probability of having empty rooms?

c) If the hotel wants only 2% probability of an overbooking situation on the Cultural Day, how many rooms should it book?

d) You have been hired as a consultant for Land Hotel. You have understood the probability structure of the overbooking problem and the next step is to advise

them on how many overbooked rooms to allow during peak season. Please make a list of the data you would need to get from the hotel in order to make your

recommendation.