Suppose you are concerned about the management of court room time, and the large number of cases that must be delayed due to failure to appear is becoming an annoyance and leading to inefficient down time.

A. If there are 10 defendants scheduled for arraignment this morning and on average 20% fail to appear and any one defendants appearance is independent of other defendants behavior, what is your best guess of the number of defendants that will this morning? (That is, what is the most likely outcome?)

B. What is the probability that all 10 appear this morning? Solve this problem using the Binomial formula. Show all of your work. (You can of course check your work with an online binomial calculator! But just a number below will be insufficient for credit)

C. You generally have time to hear 10 arraignments. Knowing that some defendants will not appear, you want to schedule more than 10 for any given morning.Explain the steps you would go through to calculate how many to schedule so that you have less than a 10% chance of having fewer than 10 arraignments to process on any given day. For this part of the problem, feel free to use an online calculator. (Such calculators facilitate a trial and error solution method) List the web site, and the values you typed in for the correct solution.

D. Our binomial probability formula relies on the fact that whether one defendant shows up is independent of whether another defendant shows up. What conditions might lead the assumption that the appearances are independent to be violated?Would dependence in appearance rates lead your answer in (c) to be too high or too low?