Question

A successful hotel is full more than half the days of the year. It is almost full most of the rest of the year and is close to empty only a few days a year. The average daily occupancy rate of the hotel is 80% with a standard deviation of 30%. The average monthly occupancy rate is the average of the daily occupancy rates, averaged over the days in a given month.

Check all the items below that describe the distribution of the average monthly occupancy rate.

	Its mean will be more than 70%
	Its mean will be between 20% and 70%
	Its mean will be less than 20%.
	Its standard deviation will be more than 20%.
	Its standard deviation will be between 3% and 20%.
	Its standard deviation will be less than 3%.
	It will be roughly bell shaped.

Answer 1

According to central limit theorem, the distribution of sample mean will be approximately normal. The average monthly occupancy rate is sampling distribution of mean. The mean of sampling distribution will be same as population mean and standard deviation of sample mean distribution (standard error) =

Average monthly occupancy rate = 80%

Standard error = = 5.5

The following are the correct options

• Its mean will be more than 70%
• Its standard deviation will be between 3% and 20%
• It will be roughly bell shaped