4.102 Delta International delivers approximately one million packages a day between East Asia and the United States. A random sample of the daily number of package delivery failures over the past six months provided the following results: 15, 10, 8, 16, 12, 11, 9, 8, 12, 9, 10, 8, 7, 16, 14, 12, 10, 9, 8, 11. There was nothing unusual about the operations during these days and, thus, the results can be considered typical. Using these data and your understanding of the delivery process answer the following:

a. What probability model should be used and why?

b. What is the probability of 10 or more failed deliveries on a typical future day?

c. What is the probability of less than 6 failed deliveries?

d. Find the number of failures such that the probability of exceeding this number is 10% or less.