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Quiz 8.1A AP Statistics Name: 1. A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that approximately 2% are defective. In a quality control procedure, we randomly select 20 toasters for testing. We want to determine the probability that no more than one of these toasters is defective. (a) Is a binomial distribution a reasonable probability model for the random variable X? State your reasons clearly. (b) Determine the probability that exactly one of the toasters is defective. (c) Define the random variable. X = . Then find the mean and standard deviation for X. (d) Find the probability that at most two of the toasters are defective. (Include enough details so that it can be understood how you arrived at your answer.) 2. Draw a card from a standard deck of 52 playing cards, observe the card, and replace the card within the deck. Count the number of times you draw a card in this manner until you observe a jack. Is a binomial distribution a reasonable probability model for the random variable X? State your reasons clearly. Chapter 8

Quiz 8.1B AP Statistics Name: In problems 1 and 2, indicate whether a binomial distribution is a reasonable probability model for the random variable X. Give your reasons in each case. 1. The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty. X is the number who say “Yes.” 2. Joey buys a Virginia lottery ticket every week. X is the number of times in a year that he wins a prize. 3. A fair coin is flipped 20 times. (a) Determine the probability that the coin comes up tails exactly 15 times. (b) Find the probability that the coin comes up tails at least 15 times. (Include enough details so that it can be understood how you arrived at your answer.) (c) Find the mean and standard deviation for the random variable X in this coin-flipping problem. (d) Find the probability that X takes a value within 2 standard deviations of its mean. Chapter 8

Quiz 8.1C AP Statistics Name: Ladies Home Journal magazine reported in 1993 that 66% of all dog owners greet their dog before greeting their spouse or children when they return home at the end of the workday. Suppose that 12 dog owners are selected at random. 1. Show that the four requirements for a binomial setting are satisfied. 2. Define the random variable: X = 3. Find the probability that exactly 7 of the 12 dog owners greet their dog first when they arrive home. 4. Find the probability that at least 5 of the 12 dog owners greet their dog first when they arrive home. 5. What is the expected number of dog owners who greet their dog first when they arrive home? 6. Find the mean and standard deviation for the random variable X in this problem. Chapter 8

Quiz 8.1D AP Statistics Name: “What do you think is the ideal number of children for a family to have?”” A Gallup poll asked this question of 1006 randomly chosen adults. Almost half (49%) thought two children was ideal. Suppose that p = 0.49 is exactly true for the population of all adults. Let X = number of adults who thought that two children was ideal. 1. Is X binomial? Check the four conditions for a binomial setting. 2. Find the mean and standard deviation of X. 3. Find the probability that X = 493. 4. Find the probability that X is within two standard deviations of the mean. 5. Describe the distribution of the binomial random variable X. 6. Would it make sense to compare your results in Question 4 with the empirical rule? Explain. 7. Use the Normal approximation to find the area between X =461 and X = 525. 8. The results in Questions 4 and 7 should be extremely close. Why would this be so? Chapter 8

Quiz 8.2A AP Statistics Name: 1. In parts (a) and (b), indicate whether a geometric distribution is a reasonable probability model for the random variable X. Give your reasons in each case. (a) Suppose that one of every 100 people in a certain community is infected with HIV. You want to identify an HIV-positive person to include in a study of an experimental new drug. How many individuals would you expect to have to interview in order to find the first person who is HIV-positive? (b) In high-profile discrimination court cases in the past, 76% of prospective jurors have been found eligible to serve on juries (that is, no objection by either the prosecution or the defense). We have 25 people in the pool of potential jurors, and we want to know if we will be successful in finding 12 people to serve on the jury from the pool. Specifically, we want to determine the probability that the 12th acceptable juror is found by the time that the 25th prospective juror is interrogated. 2. When a computerized generator is used to generate random digits, the probability that any particular digit in the set {0, 1, 2, ..., 9} is generated on any individual trial is 1/10 = 0.1. Suppose that we are generating digits one at a time and are interested in tracking occurrences of the digit 0. (a) Determine the probability that the first 0 occurs as the fifth random digit generated. (b) How many random digits would you expect to have to generate in order to observe the first 0? (c) Construct a probability distribution histogram for X = 1 through X = 5. Use the grid provided. Chapter 8

Quiz 8.2B AP Statistics Name: There is a probability of 0.08 that a vaccine will cause a certain side effect. Suppose that a number of patients are inoculated with the vaccine. We are interested in the number of patients vaccinated until the first side effect is observed. 1. Define the random variable of interest. X = 2. Verify that this describes a geometric setting. 3. Find the probability that exactly 5 patients must be vaccinated in order to observe the first side effect. 4. Construct a probability distribution table for X (up through X = 5). 5. How many patients would you expect to have to vaccinate in order to observe the first side effect? 6. What is the probability that the number of patients vaccinated until the first side effect is observed is at most 5? Chapter 8

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