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Final Review CH 5-6Name: ___________________________ Period: ___________Multiple ChoiceIdentify the choice that best completes the statement or answers the question.____1.If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon isa.random.b.predictable.c.uniform.d.probable.e.normal.____2.When two coins are tossed, the probability of getting two heads is 0.25. This means thata.of every 100 tosses, exactly 25 will have two heads.b.the odds against two heads are 4 to 1.c.in the long run, the average number of heads when two coins are tossed is 0.25.d.in the long run two heads will occur on 25% of all tosses of two coins.e.if you get two heads on each of the first five tosses of the coins, you are unlikely to get heads the fourth time.____3.A ten-sided die has each of the digits from 0 to 9 on one of its faces. Which of the following best describes what it means to say that the probability of rolling a 3 is 0.1?a.If you roll the die thousands of times, the proportion of times that you roll a 3 will be close to 0.1.b.If you roll the die 10 times, one of the rolls will be a 3.c.If you roll the die 10,000 times, 1000 of the rolls will be 3’s.d.It would be impossible to roll the die 25 times and not get any 3’s.e.If the first two rolls are 3’s, the probability of rolling a 3 on the next roll is slightly less than 0.1.____4.A basketball player makes 160 out of 200 free throws. We would estimate the probability that the player makes his next free throw to bea.0.16.b.50-50; either he makes it or he doesn’t.c.0.80.d.1.2.e.80.____5.A box has 10 tickets in it, two of which are winning tickets. You draw a ticket at random. If it's a winning ticket, you win. If not, you get another chance, as follows: your losing ticket is replaced in the box by a winning ticket (so now there are 10 tickets, as before, but 3 of them are winning tickets). You get to draw again, at random. Which of the following are legitimate methods for using simulation to estimate the probability of winning? I. Choose, at random, a two-digit number. If the first digit is 0 or 1, you win on the first draw; If the first digit is 2 through 9, but the second digit is 0, 1, or 2, you win on the second draw. Any other two-digit number means you lose.II. Choose, at random, a one-digit number. If it is 0 or 1, you win. If it is 2 through 9, pick a second number. If the second number is 8, 9, or 0, you win. Otherwise, you lose.III. Choose, at random, a one-digit number. If it is 0 or 1, you win on the first draw. If it is 2, 3, or 4, you win on the second draw; If it is 5 through 9, you lose.a.I onlyb.II onlyc.III onlyd.I and IIe.I, II, and III____6.A basketball player makes 2/3 of his free throws. To simulate a single free throw, which of the following assignments of digits to making a free throw are appropriate? I. 0 and 1 correspond to making the free throw and 2 corresponds to missing the free throw. II. 01, 02, 03, 04, 05, 06, 07, and 08 correspond to making the free throw and 09, 10, 11, and 12 correspond to missing the free throw. III. Use a die and let 1, 2, 3, and 4 correspond to making a free throw while 5 and 6 correspond to missing a free throw.a.I onlyb.II onlyc.III onlyd.I and IIIe.I, II, and III____7.Event A has probability 0.4. Event B has probability 0.5. If A and B are independent, then the probability that both events occur isa.0.0.b.0.1.c.0.2.d.0.7.e.0.9.Scenario 5-2If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color before blue M & M’s replaced tan in 1995.ColorBrownRedYellowGreenOrangeTanProbability0.30.2?0.10.10.1____8.Use Scenario 5-2. The probability of drawing a yellow candy isa.0.b..1.c..2.d..3.e.impossible to determine from the information given.____9.Use Scenario 5-2. The probability that you draw either a brown or a green candy isa..1.b..3.c..4.d..6.e..7.Scenario 5-3Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.____10.Use Scenario 5-3. The probability that at least one of the next three babies is a boy isa.0.125.b.0.333.c.0.667.d.0.750.e.0.875.____11.Use Scenario 5-3. The events A = the next two babies are boys, and B = the next two babies are girls area.disjoint.b.conditional.c.independent.plementary.e.none of the above.____12.Which of the following statements is not true?a.If two events are mutually exclusive, they are not independent.b.If two events are mutually exclusive, then P(A ? B) = 0.= 0c.If two events are independent, then they must be mutually exclusive.d.If two events, A and B, are independent, then P(A) = P(A | B).e.All four statements above are true.____13.Which of the following is not a random variable?a.The number of heads in ten tosses of a fair coin.b.The number of passengers in cars passing though a toll booth.c.The age of the driver in cars passing through a toll booth.d.The response of randomly-selected people to the question, “What is your favorite TV sit-com?”e.The response of randomly-selected people to the question, “How many hours of sleep did you get last night?’____14.Which of the following is not a random variable?a.The heights of randomly-selected buildings in New York City.b.The suit of a card randomly-selected from a 52-card deck.c.The number of children in randomly-selected households in the United States.d.The amount of money won (or lost) by the next person to walk out of a casino in Las Vegas.e.All of the above are random variables.____15.Which of the following is true about every random variableI. It takes on numerical or categorical values.II. It describes the results of a random phenomenon.III. Its behavior can be described by a probability distribution.a.I onlyb.II onlyc.III onlyd.II and IIIe.All three statements are trueScenario 6-4In the Florida scratch-card lottery, the numbers and values of prizes awarded for every 100,000 cards sold are given in the table below.Number of cardsPayoff10$1,0001000$505000$5____16.Use Scenario 6-4. The probability that a random scratch-card will pay off isa..0250.b..0601.c..2500.d..6010.e..8500.____17.Use Scenario 6-4. The expected payoff per card isa.$1.00.b.$.90.c.$.85.d.$.50.e.$.25.Scenario 6-5A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.X01234P(X)0.10.10.10.10.6____18.Use Scenario 6-5. Use The mean number of customers that make a purchase during the first hour that the store is open isa.2.0.b.2.5.c.2.9.d.3.0.e.4.0.____19.Use Scenario 6-5. The standard deviation of the number of customers that make a purchase during the first hour that the store is open isa.0.2.b.1.4.c.2.0.d.3.0.e.4.0.Scenario 6-730622678509000Suppose X is a continuous random variable taking values between 0 and 2 and having the probability density function below.____20.Use Scenario 6-7. P(X > 1.5) has valuea.0.50.b.0.33.c.0.25.d.0.125.e.0.0625.____21.The weight of written reports produced in a certain department has a Normal distribution with mean 60 g and standard deviation 12 g. The probability that the next report will weigh less than 45 g isa..1056.b..3944.c..1042.d..0418.e..8944.Scenario 6-16A poll shows that 60% of the adults in a large town are registered Democrats. A newspaper reporter wants to interview a local democrat regarding a recent decision by the City Council.____22.Use Scenario 6-16. On average, how many people will the reporter have to stop before he finds his first Democrat?a.1b.1.33c.1.67d.2e.2.33Scenario 6-17You are stuck at the Vince Lombardi rest stop on the New Jersey Turnpike with a dead battery. To get on the road again, you need to find someone with jumper cables that connect the batteries of two cars together so you can start your car again. Suppose that 16% of drivers in New Jersey carry jumper cables in their trunk. You begin to ask random people getting out of their cars if they have jumper cables.____23.Use Scenario 6-17. You’re going to give up and call a tow truck if you don’t find jumper cables by the time you’ve asked 10 people. What’s the probability you end up calling a tow truck?a.0.8251b.0.1749c.0.1344d.0.0333e.0.0280____24.At a school with 600 students, 25% of them walk to school each day. If we choose a random sample of 40 students from the school, is it appropriate to model the number of students in our sample who walk to school with a binomial distribution where n = 40 and p = 0.25?a.No, the appropriate model is a geometric distribution with n = 40 and p = 0.25.b.No, it is never appropriate to use a binomial setting when we are sampling without replacement.c.Yes, because the sample size is less than 10% of the population size.d.Yes, because and n < 30.e.We can’t determine whether a binomial distribution is appropriate unless the number of trials is known.____25.A jar has 250 marbles in it, 40 of which are red. What is the largest sample size we can take from the jar (without replacement) if we want to use the binomial distribution to model the number of red marbles in our sample?a.50b.40c.25d.4e.You can’t use a binomial distribution in this setting.Final Review CH 5-6Answer SectionMULTIPLE CHOICE1.ANS:APTS:1TOP:Idea of randomness2.ANS:DPTS:1TOP:Idea of probability/Myths3.ANS:APTS:1TOP:Idea of probability/Myths4.ANS:CPTS:1TOP:Idea of probability/Myths5.ANS:DPTS:1TOP:Simulation to estimate probability6.ANS:EPTS:1TOP:Simulation to estimate probability7.ANS:CPTS:1TOP:Multiplication Rule, Independent events8.ANS:CPTS:1TOP:Basic Probability Rules9.ANS:CPTS:1TOP:Addition of disjoint events10.ANS:EPTS:1TOP:Complement rule11.ANS:APTS:1TOP:Mutually exclusive events12.ANS:CPTS:1TOP:Independent and mutually exclusive events13.ANS:DPTS:1TOP:Identifying random variables14.ANS:BPTS:1TOP:Identifying random variables15.ANS:DPTS:1TOP:Idea of random variable16.ANS:BPTS:1TOP:Discrete random variables: probabilities from tables17.ANS:CPTS:1TOP:Mean of Discrete Random Variable18.ANS:DPTS:1TOP:Mean of Discrete Random Variable19.ANS:BPTS:1TOP:Standard deviation of Discrete R.V.20.ANS:EPTS:1TOP:Continuous rand. vars.: probabilities from density curves21.ANS:APTS:1TOP:Normal random variable probability22.ANS:CPTS:1TOP:Geometric mean23.ANS:BPTS:1TOP:Geometric probability24.ANS:CPTS:1TOP:Binomial setting and sampling25.ANS:CPTS:1TOP:Binomial setting and sampling ................
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