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Chapter 11 Review Problems

# Chapter 11 Review Problems - Chapter 11 Understanding...

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Unformatted text preview: Chapter 11 Understanding Randomness (Review) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. 1) Is the roll of a fair die random? Why or why not? 1) A) Yes. You can predict the outcome beforehand. B) No. You can usually predict the outcome on one of six attempts. C) No. A 3 or 4 is the most likely outcome. D) Yes. You cannot predict the outcome beforehand. E) No. There is always a bias in a person's rolling technique. 2) What is the minimum number of times that an ordinary deck of playing cards must be shufﬂed to 2) make the deck random? A)1 1m (3)7 D)8 E) It cannot be made random. 3) Criticize the following simulation: A student uses a random number from 5 to 13 to simulate the 3) shoe sizes of a population of females. A) The simulation will not model the real situation. It will predict too many small sizes and too many large sizes. Extremes in foot size are not all that common. B) The simulation will not model the real situation. The shoes size of a particular female is unpredictable and cannot be modeled. C) The simulation will not model the real situation. To accurately model the population, the simulation should also account for the foot width. D) The simulation should model the real situation. E) The simulation will not model the real situation. Some females have foot sizes that fall outside of the range. 4) Criticize the following simulation: A student simulates the outcome of a basketball player's 3—point shot by letting O = missed shot and 1 = made shot. A) The simulation cannot model the real situation. Shooting accuracy varies from day to day, so the real situation is inherently unpredictable. B) The simulation should model the real situation. C) The simulation will not model the real situation. The simulation fails to account for the type of defense employed by the opposing team. D) The simulation probably will not model the real situation. The shooter's accuracy on a given day might be affected by an injury or illness. E) The simulation probably will not model the real situation. The simulation assumes that the player makes 50% of his 3—point shots, which is probably unrealistic. 5) A statistics student properly simulated the number of students at her high school who have the ﬂu She then reported, "The number of students at this school with the flu is 40." What's wrong with this conclusion? A) The conclusion should indicate that the simulation suggests that there areal) students at the school who have the flu. Actual results might not match the simulated results exactly. B) The conclusion is not valid because the outcomes in the simulation are not equally likely. C) The conclusion is not valid because random numbers cannot be used to accurately model the outcome chances. D) The conclusion should indicate the number of trials used in the simulation. E) Nothing is wrong with this conclusion. 6) A tax referendum for property tax funding for a bond issue to build a new school is on the ballot in the next election. A member of the referendum committee is confident that the question will have about 52% of the votes cast in the school district. But, you're worried that only 1,000 voters will show up at the polls since this is an off—year election. How often will the referendum question lose? To find out, you setup a simulation. Describe how you will simulate a component and its outcomes. A) The component is one voter voting. An out come is a vote no for the referendum. Use three random digits, giving 000420 a yes vote and 521-999 a no vote. B) The component is one hundred voters voting. An out come is a vote yes or no for the referendum. Use one random digit, giving 0—5 a yes vote and 6~9 a no vote. C) The component is ten voters voting. An outcome is a vote yes or no for the referendum. Use two random digits, giving 0062 a yes vote and 53499 a no vote. D) The component is one voter voting. An out come is a Vote yes for the referendum. Use three random digits, giving 000699 a yes vote and 600—999 a no vote. E) The component is one voter voting. An outcome is a vote yes or no for the referendum. Use three random digits, giving 000-520 a yes vote and 521—999 a no vote. 4) 5) 6) 7) A tax referendum for property tax funding for a bond issue to build a new school is on the ballot in ’7) the next election. A member of the referendum committee is conﬁdent that the question will have about 52% of the votes cast in the school district. But, you're worried that only 1,000 voters will Show up at the polls since this is an offwyear election. How often will the referendum question lose? To find out, you setup a simulation. Describe the response variable. A) The response variable is Whether the referendum loses or not. B) The response variable is whether the referendum wins or not. C) The response variable is the yes or no vote of one random voter. D) The response variable is the number of votes for referendum that are yes. E) The response variable is the number of votes for referendum that are no. 8) When drawing five cards randomly from a deck, which is more likely, a royal flush or a full house? 8) A royal flush is the five highest cards of a single suit. A full house is three of one denomination and two of another. How could you simulate 5~carcl hands? Once you have picked one card, you cannot pick that same card again. Describe how you will simulate a trial. A) A trial is five—card hands, dealt until the deck is completely dealt. Use five sets of random numbers, ignoring repeated cards. 13) A trial is a single five—card hand. Use five sets of random numbers, ignoring repeated cards. C) A trial is a single five—card hand. Use one set of random numbers, ignoring repeated cards. D) A trial is a single card. Use random numbers, ignoring repeated cards. E) A trial is a single five—card hand. Use five sets of random numbers. Solve the problem. 9) For each time up at hat, a baseball player has a 70% chance of making an out, a 10% chance of 9) getting walked, and a 20% chance of getting a hit. Estimate the probability that, out of 5 atwbats, the player gets at least one hit. Use 30 simulation runs. A) About 70% B) 100% C) About 90% D) About 20% E) About 30% 10) In order to illustrate the basic economic and psychological dynamics involved in purchasing life insurance, one can create a very simple game with a sack, one black marble, and three white marbles. In this game, the four marbles are placed in the sack, and the player must pay a "premium" of \$5 for each draw he makes from the sack. The previously—drawn marbles are not returned to the sack. So, if he keeps playing, the player is guaranteed to win the \$12 award eventually (but at what cost?l). Use a simulation to predict the average cost to win the \$12 assuming the player continues playing until he gets the black marble. Use 30 simulation runs, letting a random number give the number of draws to obtain the black marble on a particular run. A) About \$12.50 B) About \$15.50 C) About \$20.50 :3) About \$5.00 E) About \$17.00 Z’rovide an appropriate response. '11) You take a surprise quiz in your astronomy class with 12 multiple—choice questions. You estimated that you would have about a 30% chance of getting any individual question correct. What are your chances of getting them all right? Your simulation should use at least 20 runs. A) 1728 3) 2.1074359 C) 36 D) 3.6 - s) 000000053 12) A person with type O—negative blood can donate blood to anyone who needs it, regardless of blood type. About 6% of the 5.8. population has type O~negative blood. Your workplace is hosting a blood drive this afternoon. How many potential donors do you expect they will have to examine in order to get 3 units of type (Du-negative blood? A) 50 people B) 18 people C) 729 people D) 0.18 people E) 216 people 13) Five men and three women are waiting to be interviewed for jobs. If they are all selected in random order, find the probability that all the women will be interviewed first, Your simulation should use at least 10 runs. 1 1 3 A} "5‘6" B) "55 C) "g a)?" 9 D) "21")" 56 10) ii) 12) 13) 14) Six men and three women are waiting to be interviewed for jobs. If they are all selected in random order, find the probability that the last person interviewed will be a man. Your simulation should use at least 10 runs. A)0 By; a); 13)::— mi 15) A university in your region estimates that verbal GRE scores of students who apply for admission to graduate schooi can be described by a Normal model with a mean of 550 and a standard deviation of 80. The staff in admissions open the application envelopes at random looking for 10 applicants with GRE scores over 600. How many envelopes do you think the staff will need to open? A) About 20 envelopes B) About 10 envelopes C) About 38 envelopes D) About 14 envelopes E) About 30 envelopes 16) A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws she will make in her next ﬁve free throw attempts? i. Let 0,1 represent making the first shot, 2, 3 represent making the second shot,..., 8, 9 represent making the fifth shot. Generate five random numbers 0—9, ignoring repeats. II. Let 0, 1, 2 represent missing a shot and 3, 4,.” 9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3—9. III. Let 0, 1, 2 represent missing a shot and 3, 4,..., 9 represent making a shot. Generate five random numbers 0-«9 and count how many numbers are in 3M9, ignoring repeats. A) I, 11, and III 8) II and III C) IE only D) 111 only E) I only SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 17) Brian is a systems manager for a large company. In his work, he has found that about 5% 01 17) all CDs he orders are bad. He needs to give one of the executives at his company five good CDs. Conduct a simulation to estimate how many CD3 Brian will have to check to get five good (3135 for the executive. Show three trials by clearly labeling the random number table given below. Specify the outcome for each trial and state your conclusion. 14) 15) 16) 18) Sam is preparing sweet potato pies as his dessert for Thanksgiving. The store he shops at 18) sells six sweet potatoes in a bag. He has found that each bag will contain 0, Ti, or 2 bad sweet potatoes. Based on experience he estimates that there will be no bad sweet potatoes in 40% of the bags, one bad sweet potato in 30% of the bags, and two bad sweet potatoes in the rest. Conduct a simulation to estimate how many bags Sam will have to purchase to have three dozen sweet good potatoes. Describe how you will use a random number table to conduct this simulation. 19) The Mars candy company starts a marketing campaign that puts a plastic game piece in 19) each bag of M&MS. 25% of the pieces show the ietter "M", 10% show the symbol "8:", and the rest just say "Try again". When you collect a set of three symbols "M", "tit", and you can turn them in for a free bag of candy. About how many bags will a consumer have to buy to get a free one? Use a simulation to find out. Explain how you will use the random numbers listed below to conduct your simulation. 20) Preservative Leather furniture used in public places can fade, crack, and deteriorate 20) rapidly. An airport manager wants to see if a leather preservative spray can make the furniture look good longer. He buys eight new leather chairs and pieces them in the waiting area, four near the south—facing windows and the other four setback from the windows as shown. He assigned the chairs randomly to these spots. ' El xxxxxxxxxﬁinmﬁ‘lﬁ‘ﬁfxxxx\xx Use the random numbers given to decide which chairs to spray. Explain your method clearly. 32219 00597 86374 Answer Key Testname: CHAPTER 11 UNDERSTANDING RANDOMNESS (REVIEW) 1) D 2) C 3) A 4) E 5) A 6) E 7) A 8) B 9) A 10) A 11) E 12) A 13) A 14) C 15) C 16) C 17) Let B = bad and G = good. Trial Simuiation 03|24§25|06|92|18|97728370 #1 B G G G G G 6CDs 78|69152|14|02| 85525 81183 #2 G G G G B G 6CDs 60§80|9 0%67165l 39996 81915 #3 G G G G G 5CDs According to the simulation, it will take an average of 5.7 CDs to get five good CD3. 18) {ise the digits O~3 to represent bags with 6 good sweet potatoes (norm bad), digits 4W6 to represent bags with five good sweet p0tato(one bad), and digits 7—9 to represent bags with four good sweet potatoesﬁwo bad). Look at each single digit of the random number table to determine whether you have 4, 5, or 6 good sweet potatoes in the bag. Continue this unﬁt the cumutative count is at least 36 good sweet potatoes 19) Check random numbers 2 digits at a time. Let 00—24 = "M", 25—64 a "&c", 35~99 a "Try Again". Go across the row unfit you have two M's and an &. Count the number of bags. 20) Use one digit at a time, ignoring 0, 9 and any repeated numbers. Choose two chairs from each row. (Exampie: 3, 2, 5, and 7) ...
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