Math 166:505 Fall 2013 Exam 2 - Version A

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1 Name Math 166:505 Fall 2013 Exam 2 - Version A On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work. Signature: Instructions: Part I and II are multiple choice and True/False. The multiple choice problems have only one correct answer. Please mark your answer clearly, especially if you change your answer. Any ambiguous answers will be considered incorrect. Part III is work out problems. You must show all work. Partial credit may be awarded. When possible, give your answers in exact form. If you must round, round to 4 decimal places. If multiple choice answers are given as decimals, they have been rounded to 4 decimal places. Warning: Problems are on the front and back of the page. Please work all of the problems. 1

2 Part I: Multiple Choice 1. (5 points) Bryan High School holds their annual science fair. They award a first prize, a second prize, a third prize, and three honorable mentions. If there are 65 entries, how many different ways can these 6 prizes be awarded? (a) 82,598,880 (b) 9,911,865,600 (c) x (d) None of the above 2. (5 points) A clothing store has 5 identical red shirts, 3 identical yellow shirts, 4 identical blue shirts and 7 identical pink shirts. They wish to hang them up on a rack. How many distinguishable ways can they arrange the shirts? (a) 1,396,755,360 (b) x (c) x (d) x (e) 87,091,200 (f) None of the above 3. (5 points) Seven friends go to the movies. There are four females and three males. In how many ways can they arrange themselves in a single row if they want to alternate gender? (a) 12 (b) 144 (c) 288 (d) 1225 (e) 5040 (f) None of the above 2

3 4. (5 points) In a hand of Black Jack, a player is dealt 2 cards out of a standard 52-card deck. A hand is a black jack if exactly one card is an ace and the other card is either a ten or a face card (jack, queen, king). What is the probability that a given hand is a black jack? (a) (b) (c) (d) (e) None of the above Use the following information for the next two problems: The heights of fifth grade children are normally distributed with average 56 inches and standard deviation 3 inches. 5. (5 points) What is the probability that a fifth grader is between 48 inches (4 feet) and 60 inches (5 feet) tall? (a) (b) (c) (d) (e) None of the above 6. (5 points) How tall must a fifth grader be to be in the top 10% of tallest fifth graders? (a) in. (b) in. (c) in. (d) in. (e) None of the above 3

4 7. (5 points) The Powerball lottery is a game in which 59 numbered white balls (numbered 1-59) are placed in one drum and 35 numbered red balls (numbered 1-35) are placed in another drum. Five white balls are drawn and one red ball. Participants pay $2 to guess which five white balls and which red ball will be drawn (not in any particular order). They win the jackpot if they guess all six balls correctly and win nothing otherwise. What does the jackpot need to be for the game to be fair? (a) 1,628,433,534 (b) x (c) 175,223,510 (d) 350,447,020 (e) None of the above 8. (5 points) Which of the following distributions has the smallest standard deviation? (a) (b) (c) (d) 4

5 9. (5 points) A computer password must consist of 6 characters. The first 2 must be uppercase letters, the next 2 must be digits (0-9), and the last two must be lowercase letters. How many passwords can be formed that start with a vowel? (a) 45,697,600 (b) 38,025,000 (c) 8,788,000 (d) 7,312,500 (e) None of the above 10. (2 points) A pair of unfair, six-sided dice are rolled. The random variable X is assigned the value of the sum of the uppermost faces. X is (a) finite discrete (b) infinite discrete (c) continuous 11. (2 points) A dart is thrown at a dart board. The random variable X is the distance from the dart to the bullseye. X is (a) finite discrete (b) infinite discrete (c) continuous 12. (2 points) A bag contains 50 jelly beans of assorted colors: red, green, blue, yellow, orange, and black. Jelly beans are drawn from the bag without replacement. The random variable X is the number of jelly beans you draw until you get a red one. (a) finite discrete (b) infinite discrete (c) continuous 5

6 13. (4 points) Determine whether each of the following is a binomial experiment. Circle your answer. (a) An experiment consists of flipping a fair coin 22 times and observing whether the heads is face up. Binomial Experiment Not a Binomial Experiment (b) An experiment consists of drawing 5 cards from a standard 52-card deck, without replacement, and noting whether each is a spade. Binomial Experiment Not a Binomial Experiment (c) An experiment consists of flipping an unfair coin 22 times and observing whether the heads is face up. Binomial Experiment Not a Binomial Experiment (d) An experiment consists of rolling a fair 6-sided die until a three is rolled. Binomial Experiment Not a Binomial Experiment 6

7 Part II: True/False (1 point each) 14. The number of ways that 6 people can be arranged in a single row is given by 6!. True False 15. A combination of r distinct objects taken from a set of size n is a selection of r of the objects (without concern for order). True False 16. If a random variable is infinite, it must be continuous. True False 17. The normal distribution curve touches the x-axis. True False 18. If there is a set of data that has three observations that occur with the same frequency and the frequency of these observations is also greater than the occurance of all other observations, we say the set is trimodal. True False 7

8 Part II: Work Out Problems 19. (4 points) The following is a list of the amount of rainfall in Seattle for each day of September (measured in inches). Find the mean, median, mode, and standard deviation. 0, 0.10, 0.02, 0.01, 0.94, 0.32, 0.01, 0.02, 0, 0, 0, 0, 0, 0, 0.39, 0, 0, 0, 0, 0.16, 0.01, 0.39, 0.17, 0.07, 0.07, 0.01, 0.12, 1.11, 0.82, (10 points) Taylor buys a bag of sour skittles. The bag contains 9 red skittles, 7 green skittles, 4 purple skittles, 10 orange skittles, and 5 yellow skittles. She reaches in the bag and pulls out 5 skittles at random. Red skittles are her favorite. What is the probability that at least one of her five skittles is red? 8

9 21. Visitors at a carnival pay $a to play a game. The game consists of pulling 3 balls out of a bag. The bag contains 15 balls. 5 of the balls are green, 7 are red, and 3 are blue. If one of the three balls is green, the player wins $1. If two of the balls are green, the player wins $2. If all three of the balls are green, the player wins $3. Otherwise, the player wins nothing. Let X be a random variable whose value is the net winnings of a player. (a) (8 points) Construct a probability distribution table for X. (b) (6 points) What is the minimum amount that you would expect to pay to play this game? (Hint: it is the amount that makes it a fair game) 9

10 22. A certain company employs 123 women and 97 men. Each month, one employee is selected randomly to be the employee of the month and is given the privelege of parking in a special reserved parking space. Each employee is eligible to win every month. (a) (4 points) In the year 2013, what is the probability that exactly 6 women are chosen? (b) (4 points) In the year 2013, what is the probability that between 4 and 8 woman are chosen, inclusive? (c) (4 points) What is the expected number of women chosen? 10

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