Chapter 14 Review Problems

Chapter 14 Review Problems - Chapter 14 From Randomness to...

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Unformatted text preview: Chapter 14 From Randomness to Frobabiiity (Review) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The weather reporter predicts that there is a 30% chance of rain tomorrow for a certain region. 1) What is meant by this phrase? A) Rain occurs 30% of the time in this region. B) The occurrence of rain is "truly random" and will occur 30% of the time. C) It will rain 30% of the day tomorrow. D) 30% of the time it rains on this date. 13'.) In circumstances "iike this,’i rain occurs 30% of the time. 2) A telemarketer is almost through with her entire shift, and she has not made a single sale. Her 2) manager says that she has a good chance of making a sale on her last few phone caiis because she is due. Is her manager right? A) Yes, because the Law of Averages is valid for independent events. B) No, because there is no Law of Averages for independent events. C) Yes, 1oecause the Law of Large Numbers is valid for independent events. D) No, because the Something Has to Happen Rule applies in the long—run, not in the short-run. E) No, because there is no Law of Large Numbers for independent events. Solve the problem. 3) The piastic arrow on a spinner for a child's game stops rotating to point at a color that will 3) determine what happens next. Determine whether the following probability assignment is legitimate. Probability of Red Yellow Green Blue 0.6 0.2 0.1 0.1 A) Legitimate B) Not Legitimate 4) The glastic arrow on a spinner for a child's game stops rotating to point at a color that will 4) determine what happens next. Determine whether the following probability assignment is legitimate. Probability of Red Yellow Green Blue 0.6 0.1 0.1 0.1 A) Legitimate B) Not Legitimate 5) Many stores run "secret sales": Shoppers receive cards that determine how iarge a discount they 5) get, but the percentage is revealed iiy scratching off that black stuff only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print) the distribution of discounts available. Determine whether the following probahiiity assignment is legitimate. Probability of 10% off 20% off 30% off 50% off 0 0 1.00 0 A) Legitimate i5) Not iegitimate 6) Many stores ran "secret sales": Shoppers receive cards that determine how large a discount they 6) get, but the percentage is reveaied by scratching off that black stuff only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print) the distribution of discounts available. Determine whether the following probability assignment is iegitimate. Probabiiity of 10% off 20% off 30% off 50% off 0.10 0.15 —0.10 0.85 A) Legitimate B) Not legitimate 7) In a business class, 65% of the students have never taken a statistics class, 15% have taken only one 7) semester of a statistics class, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that the first grouprnate you meet has studied at least two semesters of statistics? A) 0.15 B) 0.35 C) 0.85 D) 0.20 E) 0.80 8) An Imaginary Poll in April 2005 asked 939 U.S. adults what their main source of news was: 8) newspapers, television, internet, or radio? Here are the results: Response Number Newspapers 249 Television 389 if We select a person at random from this sample of939 adults, what is the probability that the person responded "NeWSpapers"? A) 0.112 B) 0.265 C) 0.209 D) 0.249 E) 0.414 9) In a survey of American women who were asked to name their favorite color, 19% said blue, 19% 9) said red, 16% said green, 11% said yellow, 14% said black, and the rest named another color. If you pick a survey participant at random, what is the probability that she named another color? A) 0.21 B) 0.18 (1)079 D) 0.14, E) 0.84 10) In a survey of American women who were asked to name their favorite color, 19% said blue, 16% said red, 19% said green, 12% said yellow, 13% said black, and the rest named another color. If you pick a survey participant at random, what is the probability that her favorite color is not red? A) 0.16 B) 0.74 C) 0.63 D) 0.84; E) 0.6 Solve the problem. Round your answer, as needed. 11) In a business class, 15% of the students have never taken a statistics ciass,40% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that neither of the first two groupmates you meet has studied any statistics? A) 0.85 B) 0.023 C) 0.30 D) 0.15 E) 0.45 12) In a business class, 35% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that at least one of the first two groupmates you meet has studied more than one semester of statistics? A) 0.40 B) 0.64 C) 0.16 D) 0.60 E) 0.36 13) An Imaginary Poll in January 2005 asked 11% US. adults how likely they were to see a new movie that was coming out in the summer. Here's how they responded: Response Number Will definitely see it 210 Will probably see it 266 Will probably not see it 346 Will definitely not see it 372 Total 1194 Let's call someone who responded that they would definitely or probably see it a "likely viewer" and the other two categories, "unlikely viewer." if we select two people at random from this sample, what is the probability that neither is a likely viewer? A) 0.601 B) 0097' C) 0.084 o) 0.362 12) 0.159 14) Opinion-«polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 74% of US. households, while the percentage of those contacted who agree to cooperate with the survey is 36%. Each household, of course, is independent of the others. What is the probability that the next household on the list will be contacted but will refuse to cooperate? A) 0.474 B) 0.094 C) 0.266 D) 0.166 E) 0.192 15) Opinion~polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 74% of US. households, while the percentage of those contacted who agree to cooperate with the survey isSZ‘i/o. Each household, of course, is independent of the others. What is the probability of obtaining an interview with the next household on the sample list? A) 0.083 B) 0.503 C) 0.740 D) 0.177 E) 0.237 is) 11) 12) 13) it) 15) 16) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 16) 30% are defective. if three of the products are randomly selected, find the probability that all of them are acceptable. A) 0.429 B) 0.027 C) 0.34.3 D) 2.1 E) 0.9 1'7) A study conducted at a certain college shows that 56% of the school's graduates find. a job in their 17) chosen field within a year after graduation. Find. the probability that a1nong9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. A) 0.995 B) 1.00 C) 0.560 D) 0.999 E) 0.111 18) 'l'here is a huge pile of buttons in which 30% are black, 15% are blue, 16% are orange, 22% are 18) white, and the rest are clear. You close your eyes, choose a button at random, write down what color it is, and then put it back in the pile. What is the probability that the third button you choose is the first one that's blue? A) 0.614 B) 0.108 C) 0.019 D) 0.003 E) 0.135 19) You roll a fair die six times. What is the probability that you roll all 5'3? 19) A) 0.167 B) 0833 C) 1 D) 1.2 E) 0.00002 20) You roll a fair die three times. What is the probability that the numbers you roll are not aliZ's? 20) A) 0.421 B) 0.579 C) 0.005 D) 0.995 E) 0.833 Determine whether the events are disjoint, independent, neither, or both. 21) in rolling a fair die once, the events of getting a 2 and getting a 1 21) A) Disioint 3) independent C) Neither D) Both 22) In rolling a fair die twice, the events of getting a 1 on the first roll and a 4 on the second 22) A) Disjoint B) Independent C) Neither D) Both 23) One bait is removed from a bag containing 1 blue ball, 1 red ball, 1 yellow ball, and 1 green ball. 23) Without returning the first bail to the bag a second ball is removed. A) Disjoint B) Independent C) Neither D) Both 24) In driving a car, the events of driving over the speed limit and getting a speeding ticket 24) A) Disjoint B) Independent C) Neither D) Both Provide an appropriate response. 25) A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads 25) on the next flip is... A) greater than 50%, since it appears that we are in a streak of "heads." B) 50%. C) it cannot be determined. D) iess than 50%, since "tails" is due to come up. E) 100% 26) According to the National Teiecommunication and Information Administration, 50.5% of US. 26) households had Internet access in 2001. What is the probability that four randomly selected US. househoids ail had Internet access in 2001? A) 49.5% B) 12.6% C) 93.5% D) 50.5% E) 6.5% SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 27) You believe that there is a 20% chance that you will earn an A in your English ciass, a 10% 2'7) chance that you wilt earn an A in your Physics class, and a 5% chance that you wili earn an A in both classes. Are "earning an A in English" and "earning an A in Physics" disjoint events? Explain. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 28) Which two events are most likely to be independent? 28) A) being a senior; going to homeroom B) having 3 inches of snow in the morning; being on time for schooi C) doing the Statistics homework; getting an A on the test D) registering to vote; being leftwhanded E) having a car accident; having a junior license 29) Pepsi is running a sales promotion in which 12% of all bottles have a "FREE" logo under the cap. 29) What is the probability that you find two free ones in a 6—pack? A) 23% B) 1% C) 11% D) 97% E) 13% 30) An ice cream stand reports that 12% of the cones they seli are "jumbo" size. You want to see what a 30) "jumbo" cone looks like, so you stand and watch the sales for a while. What is the probabiiity that the first jumbo cone is the fourth cone you see them sell? A) 60% B) 40% C) 33% D) 8% E) 93% 31) A friend of yours plans to toss a fair coin 200 times, You watch the first 20 tosses and are surprised 31) that she got 15 heads. But then you get bored and leave. How many heads do you expect her to have when she has finished at} 200 tosses? A) 150 B) 110 C) 115 o) 100 E) 105 Answer Key Testname: CHAPTER 14 FROM RANDOMNESS TO PROBABILITY(REVIEW) 1) E 2) B 3) A 4) B 5)A 6) B 7) D 8) B 9) A 10) D 11) B 12) B 13) D 14) A 15) E 16) C 1'7) D 18) B 19) E 20) D 21) A 22) B 23) A 24) C 25) B 26) E 27) These are not disjoint events since you can earn an A in English and an A in Physics. Engiish 15% 28) D 29) E 30) D 31) E ...
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Chapter 14 Review Problems - Chapter 14 From Randomness to...

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