1. A Math test consists of 40 true/false questions. Find that how many different possible answer keys can be made. 2. Most of us love Philippine 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. Average person who drives car in United States drives 12, 400 which is 50% more than an average driver in Europe. We assume that the number of yearly miles by U.S. drivers is approximately a normal random variable of standard deviation of 3800 miles. Calculate percent of drivers who traveled between 10,000 to 15,000 miles in a year. 4. Of the Statistics graduates of a University 40%, received a starting salary of $45,000.00. If 6 of them are randomly selected, find the probability that all the graduated had starting salary of $45,000.00. 5. 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 win a single small prize? 6. At men's clothing store, 12 males bought green sweaters, 8 purchased blue golf sweaters, 4 bought white sweaters and 7 decided to by gray sweaters. If a customer is selected at random, calculate the probability that he bought: (a) Green sweater (b) blue sweater or white (c) blue or gray or white (d) A sweater which was not gray. Important: Please read carefully....... You are allowed to use technology for the following Problems (Problem #7 and Problem #8), and these two Problems only. Most probably, you have to use technology or you may have to spend hours, to carry out the necessary calculations by hand. Nonetheless, you should clearly delineate and explain your logic and reasoning on how to tackle these two problems. 7. The Undesirable Air Lines (UAL???) is notorious for its cost-cutting substandard customer service. Consequently, only 85% of the ticket holders will show up for a flight. The Air Lines workhorse, the Boring 878, has 234 seats. UAL, of course, will make extra money by overbooking. However, they have to worry about the FAA fines, and they have to keep a safety margin, say, that there is at least 95% probability that they can accommodate all those who show up for the Boring 878 flight. How many seats can they actually sell in this case? 8. It is an open secret that airlines overbook flights, but I have just learned recently that bookstores underbook (I might have invented this new term.) textbooks.......... To make a long story short, our designated virtual bookstore, BOOKS Direct, routinely, as a matter of business practice, orders less textbooks than the amount requested by the Registrar's Office. That is what I have figured out....... Simply put, BOOKS Direct has to "eat" the books if they are not sold. Do you want to eat the books? You may want to cook the books before you eat them! Oops, I hope there is no account major in this class? OK, let us cut to the chase..... BOOKS Direct believes that only 85% of our registered students will stay registered in a class long enough to purchase the required textbook. Let's pick on our STAT 200 students. According to the Registrar's Office, we have 600 students enrolled in STAT 200 this spring 2014. Suppose you are the CEO of BOOKS Direct, and you want to perform a probability analysis. What would be the number of STAT 200 textbook bundles you would order so that you stay below 5% probability of having to back-order from Pearson Custom Publishing? (Note: Our Provost would be very angry when she hears that textbook bundles have to be back-ordered. In any case, by next fall, we will no longer need the service of BOOKS Direct as we are moving 100% to free eResources