Basic Probability & Statistics Exam 2 { Part I { Sections (Chapter 4, Chapter 5) March 19, 2009

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1 NAME: INSTRUCTOR: Dr. Bathi Kasturiarachi Math Spring 2009 Basic Probability & Statistics Exam 2 { Part I { Sections (Chapter 4, Chapter 5) March 19, 2009 Read through the entire test before beginning. Make sure you have 6 pages. You must use your calculator. Please be sure to show your work. Unsupported answers will be counted as incorrect. Please ASK if something is unclear or confusing. Each question is worth 05 points. Relax and do your best. GOOD LUCK!!! You may use the formulas provided below. Remember to sign the pledge at the bottom of this page. YOU ARE NOT ALLOWED TO DISCUSS THIS EXAM WITH ANYONE ELSE, NOR CAN YOU USE THE INTERNET OR OTHER TEXTS. The only allowed help are your notes and our text. Please circle your nal answer for each question. PROBLEM POINTS 01 /5 02 /5 03 /5 04 /5 05 /5 06 /5 07 /5 08 /5 09 /5 10 /5 11 /5 12 /5 13 /5 14 /5 15 /5 16 /5 17 /5 18 /5 19 /5 20 /5 Formulas: = E(X) = X X P (X) 2 = X [X 2 P (X)] 2 P (X = r) = (ncr) p r (1 p) n r For a binomial distribution: = np; = p np(1 p) Total /50 PLEDGE: I pledge that I never gave nor received any unauthorized help in this exam. SIGNATURE: 1

2 1. What is the set of a single possible outcome of a probability experiment called? (a). (b). (c). (d). statistic sample space event Venn diagrams 2. It is estimated that Lebron James makes 160 out of 200 free throws. We would estimate the probability that Lebron will make his next free throw to be: (a) (b). (c) (d) , either makes it or doesn't 3. A coin is tossed 5 times. What is the probability of getting at least one head? 4. The outcome of event A does not inuence the outcome of event B. Events A and B are called: (a). (b). (c). (d). mutually exclusive dependent disjoint independent 5. In the game of roulette, a wheel consists of 38 slots numbered 0; 00; 1; 2; 3; ; 35; 36. The odd numbered slots are red, and the even numbered slots are black. The numbers 0 and 00 are green. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. (a) What is the probability that the metal ball lands on green or red? (b) What is the probability that the metal ball does not land on green? 2

3 6. A drawer contains six black socks, four brown socks, and two green socks. Suppose that two socks are drawn from the drawer without replacing the rst. Carefully draw a tree diagram and determine the probability of getting two brown socks. 7. If you draw an M& M candy from a bag of M& M candies, the candy you will draw is one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the probabilities are as given below. Color Brown Red Yellow Green Orange Tan Probability ? (a) The probability of drawing a yellow candy is: (b) The probability that you will NOT draw a red candy is: (c) The probability that you will draw either a brown OR green candy is: 8. Compute the probability that at least 1 male out of 1000 aged 24 years will die during the course of the year if the probability that a randomly selected 24-year-old male survives the year is

4 9. A company is testing a new medicine for migraine headaches. In the study, 150 women were given the new medicine and 100 women were given a placebo. Each participant was directed to take the medicine when the rst symptoms of a migraine occurred and then to record whether the headache went away within 45 minutes or lingered. The results are recorded in the following table. Headache went away Headache lingered Given medicine Given placebo (a) If a study participant is selected at random, what is the probability that her headache went away within 45 minutes? (b) If a study participant is selected at random, what is the probability that she was given the placebo and her headache went away within 45 minutes? (c) If a study participant is selected at random, what is the probability that she was given the placebo or her headache went away within 45 minutes? 10. A UPS delivery route must include stops in ve locations in a city. How many dierent routes are possible? Explain. 11. There are 9 members on the board of directors at Akron General Hospital. If they must select a chairperson, vice-chairperson, and a secretary, how many possibilities are there? Show all the work. Questions # 12 & # 13 are connected About 13% of the population is left handed. 12. If two people are randomly selected, what is the probability both are left handed? 13. If two people are randomly selected, what is the probability at least one is right handed? 4

5 14. In the Illinois Lottery, a large urn contains balls numbered 1 to 54. From this urn, 6 balls are randomly chosen without replacement. For a $ 1 bet, a player chooses two sets of 6 numbers. To win, all six numbers (in either set) must match those chosen from the urn. The order in which the balls are selected does not matter. What is the probability of winning? 15. Does the following determine a probability distribution? Explain. x P (x) According to the National Endowment of Arts, 21% os U.S. women attended a musical play in In a random sample of 15 U.S. women, what is the probability that exactly 5 have attended a musical play in 2003? [HINT: You may assume the distribution is binomial, and use formula.] 17. A binomial distribution has n = 9 and p = 1 3. Find the mean and standard deviation of this distribution. 18. Use the binomial probability Table B to nd the probability of getting at least three correct responses among 5 dierent requests from AT& T directory assistance. Assume that in general, AT& T is correct 90% of the time. That is, nd P (X 3). 5

6 19. When randomly selecting a jail inmate convicted of DWI (driving while intoxicated), the probability distribution for the number X of prior DWI sentences is as described in the accompanying table. Find the mean and standard deviation of this distribution. X P (X) X P (X) X 2 X 2 P (X) An investor has 0.60 probability of making a $ prot and a 0.40 probability of suering a $ loss. What is the expected value? Should she make the investment based on the expected value? 6

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