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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. The quiz is due by midnight, Sunday, June 28, Eastern Daylight Saving Time.

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.

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http://www.umuc.edu/policies/academicpolicies/aa15025.cfm
http://www.umuc.edu/policies/academicpolicies/aa15025.cfm
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 team of 5 has to be picked randomly from the crew of 7 boys and 3 girls.

a. What is the probability that all 3 girls are picked in this team of 5? b. What is the probability that none of the girls are picked in this team of 5? c. What is the probability that 2 of the girls are picked in this team of 5?

4. (10 points) In this economically challenging time, yours truly, CEO of the Outrageous Products Enterprise, would like to make extra money to support his frequent filet-mignon-and- double-lobster-tail dinner habit. A promising enterprise is to mass-produce tourmaline wedding rings for brides. Based on my diligent research, I have found out that women's ring size normally distributed with a mean of 6.0, and a standard deviation of 1.0. I am going to order 5000 tourmaline wedding rings from my reliable Siberian source. They will manufacture ring size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5. How many wedding rings should I order for each of the ring size should I order 5000 rings altogether? (Note: It is natural to assume that if your ring size falls between two of the above standard manufacturing size, you will take the bigger of the two.)

http://polaris.umuc.edu/%7Eaau/crying_baby.html
5. (5 points) A soda company want to stimulate sales in this economic climate by giving customers a chance to win a small prize for ever bottle of soda they buy. There is a 20% chance that a customer will find a picture of a dancing banana ( ) at the bottom of the cap upon opening up a bottle of soda. The customer can then redeem that bottle cap with this picture for a small prize. Now, if I buy a 6-pack of soda, what is the probability that I will win something, i.e., at least winning a single small prize?

6. (5 points) When constructing a confidence interval for a population with a simple random sample selected from a normally distributed population with unknown σ, the Student t- distribution should be used. If the standard normal distribution is correctly used instead, how would the confidence interval be affected?