STAT 200 Fall 2015 Quiz #2 Please answer all 12 questions. The maximum score for each question is posted at the beginning of the question, and the maximum score for the quiz is 80 points. Make sure your answers are as complete as possible and show your work/argument. In particular, when there are calculations involved, you should show how you come up with your answers with necessary tables, if applicable. Answers that come straight from program software packages will not be accepted. Quizzes submitted after the due date will receive a grade of zero (0). IMPORTANT: Per the direction of the Dean's Office, you are requested to include a brief note at the beginning of your submitted quiz, confirming that your work is your own. By typing my signature below, I pledge that this is my own work done in accordance with the UMUC Policy 150.25 - Academic Dishonesty and Plagiarism (http://www.umuc.edu/policies/academicpolicies/aa15025.cfm) on academic dishonesty and plagiarism. I have not received or given any unauthorized assistance on this assignment/examination. _________________________ Electronic Signature Your submitted quiz will be accepted only if you have included this statement. 1. (10 points) Once upon a time, I had a fast-food lunch with a mathematician colleague. I noticed a very strange behavior in him. I called it the Au-Burger Syndrome since it was discovered by me at a burger joint. Based on my unscientific survey, it is a rare but real malady inflicting 2% of mathematicians worldwide. Yours truly has recently discovered a screening test for this rare malady, and the finding has just been reported to the International Association of Insane Scientists (IAIS) for publication. Unfortunately, my esteemed colleagues who reviewed my submitted draft discovered that the reliability of this screening test is only 80%. What it means is that it gives a positive result, false positive, in 20% of the mathematicians tested even though they are not afflicted by this horribly-embarrassing malady. I have found an unsuspecting victim, oops, I mean subject, down the street. This good old mathematician is tested positive! What is the probability that he is actually inflicted by this rare disabling malady? 2. (5 points) Most of us love Luzon mangoes, but hate buying those that are picked too early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of having 15% of the picked rot upon arrival at the packing facility. If the packing process is all done by machines without human inspection to pick out any rotten mangos, what would be the probability of having at most 2 rotten mangos packed in a box of 12? 3. (5 points) We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance tea.