Chapter 6 Review (6.1-6.2) Chapter 6 Test B Multiple Choice Note: Some questions require the use of either a standard normal probability table or technology that can calculate normal probabilities. Section 6.1 (Probability Distributions are Models of Random Experiments) 1. [Objective: Distinguish between discrete and continuous-valued variables] Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24-hour period. a. Continuous b. Discrete 2. [Objective: Distinguish between discrete and continuous-valued variables] Determine whether the variable would best be modeled as continuous or discrete: The temperature of a cup of coffee dispensed from a beverage vending machine, taken four times during a 24-hour period. a. Continuous b. Discrete 3. [Objective: Understand the uniform probability distribution] At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last sixteen minutes or more? What is the probability that the speech will last between eighteen and nineteen minutes? a. b. c. d. Can t be determined with the given information 0.50; 0.75 0.75; 0.25 0.50; 0.25
6-2 Chapter 6 Test B 4. [Objective: Understand the properties of a probability distribution] A box containing recipes from five categories is dropped so that the recipe cards are thoroughly mixed up. The following table shows the possible categories and the associated probability for a recipe randomly chosen. Does the table represent a probability distribution? Category Probability Main Dish 0.421 Appetizer 0.210 Desert 0.103 Salad 0.173 Vegetable 0.093 a. Yes b. No c. Can t be determined with the given information Section 6.2 (The Normal Model) Use the following information for questions (5)-(7). Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. 5. [Objective: Apply the normal model to find probabilities] Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to the nearest tenth of a percent. a. Roughly 15.1% of the basketballs will weigh more than 23.1 ounces. b. Roughly 42.3% of the basketballs will weigh more than 23.1 ounces. c. Roughly 36.4% of the basketballs will weigh more than 23.1 ounces. d. Roughly 13.6% of the basketballs will weigh more than 23.1 ounces. 6. [Objective: Apply the normal model to find probabilities] If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth. a. 0.547 b. 0.315 c. 0.685 d. 0.723 7. [Objective: Apply the normal model to find probabilities] Would it be unusual to randomly select a regulation basketball and find that it weighs 23.75 ounces? a. Yes, this would be unusual. b. No, this would not be unusual.
Chapter 6 Test B 6-3 8. [Objective: Apply the normal model to find probabilities] Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement. a. Approximately 95% of all Benneke brand canned peaches will weigh between 12.85 ounces and 14.15 ounces. b. The probability that a randomly selected can of Benneke peaches will weigh between 12.9 ounces and 13.6 ounces is approximately 0.585. c. About 4% of all cans of Benneke peaches will weigh less than 12.9 ounces d. All of the above statements are true. Use the following information for questions (9) - (11). The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. 9. [Objective: Apply the normal model to find probabilities] Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 15.5 minutes? Round to the nearest whole percent. a. 37% b. 63% c. 25%. 10. [Objective: Distinguish between a percentile and a measurement] Which of these statements is asking for a probability? a. What percentage of people living and working in Kokomo has a travel time to work that is between thirteen and fifteen minutes? b. If 15% of people living and working in Kokomo have travel time to work that is below a certain number of minutes, how many minutes would that be?
6-4 Chapter 6 Test B 11. [Objective: Calculate a data value from a percentile or z-score] Suppose that it is reported in the news that 8 % of the people living and working in Kokomo feel very satisfied with their commute time to work. What is the travel time to work that separates the bottom 8% of people with the shortest travel times and the upper 92%? Round to the nearest tenth of a minute. a. 17.2 minutes b. 13.8 minutes c. 10.7 minutes 12. [Objective: Calculate a data value from a percentile or z-score] The normal model N ( 58,21) describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z-score of -2.01. What is the weight of this egg in grams? Round to the nearest hundredth of a gram. a. 31.20 grams b. 15.80 grams c. 28.50 grams d. 38.10 grams Section 6.3 (The Binomial Model) 13. [Objective: Understand the binomial model] Which of the following characteristics are not required for the binomial model? a. The probability of success and of failure must be equal. b. There are a fixed number of trials. c. The trials must be independent. d. The probability of success is the same at each trial. 14. [Objective: Understand the binomial model] Determine which of the given procedures describe a binomial distribution. a. Record the number of songs downloaded in a month for a group of 30 randomly selected college students. b. Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58. c. Surveying customers entering a sporting equipment store until a customer responds that he or she was shopping for a bicycle. Use the following information to answer questions (15)-(18). Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket. 15. [Objective: Calculate probabilities using the binomial model] What is the probability that exactly seven out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth. a. 0.035 b. 0.480 c. 0.998 d. 0.264
Chapter 6 Test B 6-5 16. [Objective: Calculate probabilities using the binomial model] What is the probability that at least nine out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth. a. 0.065 b. 0.183 c. 0.935 d. 0.857 17. [Objective: Calculate probabilities using the binomial model] What is the probability that no more than three out of ten people used an online travel website when they book their airline ticket? Round to the nearest thousandth. a. 0.733 b. 0.115 c. 0.007 18. [Objective: Calculate the mean and standard deviation using the binomial model] Out of ten randomly selected people, how many would you expect to use an online travel website to book their hotel, give or take how many? Round to the nearest whole person. a. 7 people, give or take 1 person b. 8 people, give or take 2 people c. 7 people, give or take 2 people d. 3 people, give or take 4 people 19. [Objective: Calculate probabilities using the binomial model] Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and three of your friends each draws a chip (with replacement), what is the probability that at least one of your group of four will win the valuable prize? Round to the nearest thousandth. a. 0.870 b. 0.130 c. 0.758 20. [Objective: Understand expected value and the binomial model] Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked Do you buy at least one tabloid magazine per week?, would you be surprised if 45 or more said yes to this question? Why? a. Yes, 55 would be an unusually small number of people given the known probability of 0.115. b. No, 55 is within the expected range of people. c. Yes, 55 would be an unusually large number of people given the known probability of 0.12. d. Cannot be determined with the given information.