What is the income distribution of super shoppers? A supermarket super shopper is dened as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars. Income ran e 5-15 15-25 25-35 35-45 45-55 55 or more Mldpolnt x 10 20 30 40 50 60 Percent of super shogpers 21% 13% 22% 17% 20% 7% USE (a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain. Yes. The evens are distinct and the probabilities do not sum to 1. Yes. The events are distinct and the probabilities sum to 1. Yes. The events are indistinct and the probabilities sum to less than 1. " No. The evens are indistinct and the probabilities sum to more than 1. No. The events are indistinct and the probabilities sum to 1. (b) Use a histogram to graph the probability distribution of part (a). (Because the data table has summarized the data into categories, use SALT to create a bar chart.) 20 20 I Supt shppra I Supt shppra lo 10 d) 8 u I: H Income i Supt Shppr: i Supt Shppr: 10 10 Income 0 S u c H (c) Compute the expected income M of a super shopper. (Round your answer to two decimal places.) [4 = thousands of dollars (d) Compute the standard deviation 0 for the income of super shoppers. (Round your answer to two decimal places.) a = thousands of dollars Need Help? BBBASICSTAT8 6.2.003. | MY NOTES For a binomial experiment, how many outcomes are possible for each trial? What are the possible outcomes? 3. [-/2 Points] A one; success \" two; success or failure three; success, failure, or neither A one; failure Need Help? 4. [-/2 Points] DETAILS BBBASICSTAT8 6.2.008. MY NOTES In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice? Check each of the requirements of a binomial experiment and give the values of n, r,and p. Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6 Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 2, r = 5, p = 1/6 Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/5 No. The five trials are independent, but have more than two outcomes. Need Help? Read It5. [-I12 Points] BBBASICSTAT8 6.2.016.MI.S. PRACTICE ANOTHER Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has ve answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all eight questions, nd the indicated probabilities. (Round your answers to three decimal places.) m USE (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions incorrectly? (c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table. Then use the fact that P(r 2 1) = 1 P(r = 0). Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference? ' They should not be equal, but are equal. ' They should be equal, but may differ slightly due to rounding error. ' They should be equal, but may not be due to table error. " They should be equal, but differ substantially. (d) What is the probability that Richard will answer at least half the questions correctly? 6. [16 Points] BBBASICSTAT8 6.3.005. Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about 6.9. Use the criterion that it is unusual to have data values more than 2.5 standard deviations above the mean or 2.5 standard deviations below the mean to answer the following questions. (a) Would it be unusual to have more than 120 successes out of 200 trials? Explain. Yes. 120 is more than 2.5 standard deviations above the expected value. Yes. 120 is more than 2.5 standard deviations below the expected value. '\\ No. 120 is less than 2.5 standard deviations above the expected value. No. 120 is less than 2.5 standard deviations below the expected value. (b) Would it be unusual to have fewer than 40 successes out of 200 trials? Explain. Yes. 40 is more than 2.5 standard deviations above the expected value. Yes. 40 is more than 2.5 standard deviations below the expected value. No. 40 is less than 2.5 standard deviations above the expected value. '\\ No. 40 is less than 2.5 standard deviations below the expected value. (c) Would it be unusual to have from 70 to 90 successes out of 200 trials? Explain. No. 90 observations is more than 2.5 standard deviations above the expected value. Yes. 70 observations is more than 2.5 standard deviations below the expected value. No. 70 to 90 observations is within 2.5 standard deviations of the expected value. Yes. 70 to 90 observations is within 2.5 standard deviations of the expected value. Need Help? 7. [-/6 Points] DETAILS BBBASICSTAT8 6.3.016.S. MY NOTES PRACTICE ANOTHE Do you tailgate the car in front of you? About 45% of all drivers will tailgate before passing, thinking they can make the car in front of them go faster. Suppose that you are driving a considerable distance on a two-lane highway and are passed by 10 vehicles. LO USE SALT (a) Let r be the number of vehicles that tailgate before passing. Make a histogram showing the probability distribution of r for r = 0 through r = 10. 0.25- 0.35 1 0.3 0.2 0.25 0.15 0.2- P (r) P (r) 0.1 0.15- 0.1- 0.05 0.05 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 O O 0.25 0.2 0.2- 0.15 P (r) P (r) 0.15 0.1 0.1- 0.05- 0.05- 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 O OP(r) 012345678910 012345676910 m t '\\ r (b) Compute the expected number of vehicles out of 10 that will tailgate. vehicles (c) Compute the standard deviation of this distribution. (Round your answer to two decimal places.) vehicles