1.Budget Airlines is a seasonal airline that operates flights from Myrtle Beach, South Carolina, to various cities in the northeast. The destinations include Boston, Pittsburgh, Buffalo, and both LaGuardia and JFK airports in New York City. Recently Budget has been concerned about the number of lost bags. Ann Poston from the Analytics Department was asked to study the issue. She randomly selected a sample of 500 flights and found that a total of twenty bags were lost on the sampled flights. Assume that this situation follows the Poisson distribution. What is the mean number of bags lost per flight? What is the likelihood that no bags are lost on a flight? What is the probability at least one bag is lost?

2.Suppose you want to buy a restaurant. So you asked the owner what is the distribution of the number of customers you get each work day. The owner gave you the distribution (expected percentages) on each work day in the following table. And you observed the number of customers on each work day by yourself which are also listed as below.

MonTuesWedThursFri

Expected 10% 10% 15% 20% 45%

Observed 30 14 34 45 57

Do you think the owner's distribution is correct or not? Please explain why.