## Statistics Spring 2014 Test 1, version 2

Name: ___________________________________________________________

All these questions are about a remote town of Paso El, which has absolutely nothing to do with our beloved city -- except that both have universities.

2. In the cheapest on-campus cafeteria, students are offered a 3-dish full meal: a soup, a main dish, and a desert. If one of these dishes is inedible, the student gets a discount coupon for the next day's lunch. The probability that a soup is inedible is 10%, that the main dish is inedible is 20%, and the probability that the desert is inedible is only 5%. What percentage of students gets a discount coupon?

3. An average student likes four out of six meals on a menu and hates the other two choices. A restaurant marks two of the menu items as today's specials, available at a special discount. What is the percentage of students who will use this discount?

5. A picky student goes to a new ethnic restaurant (e.g., Bhutanese) which has six main dishes on the menu. With each main dish, the student can select one of the three side dishes. All the dishes' names are in the corresponding foreign language, so the poor student does not have a clue on what he chooses. From his experience, the student knows that on average, he likes half of the main dishes and two thirds of the side dishes. What is the probability that the student will like the selected meal? If this student comes the second day and orders a completely different meal, what is the probability that he will be happy on both days?

6. To make it interesting, two student friends play a game. To decide which of three closest-to-department restaurants #0, #1, and #2 to go to, they flip two coins, counting head as 1 and tail as 0. On an even day, the students take the sum s of the resulting two random numbers; on odd days, they take the absolute value v of the difference of these numbers -- and this is the place where they go to have lunch. What is the probability that s = 2 if v = 1? if v = 0? Are the variables s and v independent? Explain your answer.

7. A picky new student tries all near-campus restaurants until she finds one which is perfectly to her taste. From her experience, she knows that, on average, she likes only 20% of the restaurants. On average, how many restaurants will she try before she find a restaurant that she likes?

8. On average, a student eats 2,000 calories a day, with a standard deviation of 500. What is the probability that 25,600 students from the Paso El university eat less than 500,000,000 calories a day? Hint: Use Central Limit Theorem.

9. In the city of Paso El, there are 8 fast-food restaurants near campus, 5 tolerable and 3 not good. A freshman student has no idea which restaurants are good and which are not, so every day, he selects, at random, a restaurant which is different from what he visited before. In 3 days, what is the probability that all 3 restaurants visited by the student are tolerable? What is the probability that all 3 restaurants will be not good? What is the expected value and variance of the number of tolerable restaurants among the ones the student visited in 3 days?