As a FedEx contractor, you own 50 trucks. Ten of your trucks are brandnew, and each of these trucks has a 95% chance of being in service onany particular day. Twenty of your trucks are of an intermediate age, andeach of these trucks has a 90% chance of being in service on any particularday. Finally, twenty of your trucks are old; each truck has a 80% chanceof being in service on any particular day. You need at least 44 trucks tobe in service in order to meet your delivery goals.
(a) Using your probability formulas, calculate what the average (i.e. ex-pected) number of trucks will be serviceable on any given day. Showyour work. (5 pts)
(b) What is the probability that you have enough trucks (i.e. that youhave 44 or more trucks)? Use Excel to conduct a simulation with20,000 trials in order to answer this. (5 pts)
(c) Repeat the above exercise, once for each of the following quantities:30, 35, 40, 43, 44, 45, 50. Plot your answers on a line graph, with theprobability on the y-axis, and the quantities on the x-axis. Be sureto title your graph and provide axis labels. Note, your graph shouldbe sloping downward or upward, but it shouldn’t zig-zag upward anddownward. Such zig-zags can happen because of random error fromthe simulations. Be sure to conduct enough trials in your simulationsso that your graph doesn’t zig-zag (i.e. it should be monotonic).