Problem 1 A downtown hotel runs a special promotion to try to fill rooms that aren't usually occupied on weekends. The long-run average response is 71 rooms per weekend. There is considerable variation due to weather, competing attractions, and unknown cases. The standard deviation of responses is about 15 rooms. a) The hotel schedules adequate staff to handle a response of 80 rooms. If more guests arrive, additional stuff must be brought in at overtime rates. What is the probability that additional staff will be needed on the particular weekend? b) The promotion manager reviews response rates for blocks of 30 weekends, which is regarded as a random sample. Completely describe the sampling distribution of the sample mean. c) If the average demand over the 30- week sample exceeds 80, the manager will increase the scheduled staff. What is the probability that a 30- week sample mean will exceed 80? d) Answering (a) and (c) do you have to make any assumptions about population . Explain why or why not. e) If the average demand over the 30 week sample is 90 rooms, is this is unusual? What conclusion might you draw