The post office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. answer the following questions based on this information:

a. if you mail eight local letters, what is the probability that all of them will be delivered the next day?
b. if you mail eight local letters, what is the average number you expect to be delivered the next day?
c. calculate the standard deviation of the number delivered when 8 local letters are mailed.
d. when there are 8 local letters mailed, what is the probability that the number delivered will be within 2 standard deviations of the mean?

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)