A pizza chain records how long it takes customers to receive their delivery orders. Suppose the distribution of these delivery times is strongly skewed to the left with a mean of 30 minutes and a standard deviation of 10 minutes. Management plans on calculating the mean delivery time from a random sample of 25 orders. We can assume independence between orders in the sample. What is the probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population 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.)