Exam Chapters 4&5 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? 1) Find the indicated probability. 2) A study of consumer smoking habits includes 198 people in the 18-22 age bracket (40 of whom smoke), 125 people in the 23-30 age bracket (31 of whom smoke), and 90 people in the 31-40 age bracket (30 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes. 2) 3) The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Occasional smoker Regular smoker Heavy smoker Total Men 431 50 71 49 601 Women 382 48 86 39 555 Total 813 98 157 88 1156 If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy smoker. 4) In a poll, respondents were asked whether they had ever been in a car accident. 215 respondents indicated that they had been in a car accident and 449 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth, if necessary. 3) 4) 5) The data set represents the income levels of the members of a country club. Find the 5) probability that a randomly selected member earns at least $77,000. Round your answers to the nearest tenth. 93,000 109,000 75,000 117,000 76,000 93,000 77,000 73,000 133,000 173,000 74,000 85,000 125,000 76,000 109,000 101,000 77,000 141,000 72,000 101,000 6) The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4 of the 8 Coffleton residents recognize the brand name. 6) 7) A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four decimal places. 7) 8) In one town, 44% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary. 8) 1
9) Refer to the table which summarizes the results of testing for a certain disease. Positive Test Result Negative Test Result Subject has the disease 85 7 Subject does not have the disease 28 153 If one of the results is randomly selected, what is the probability that it is a false positive (test indicates the person has the disease when in fact they don't)? What does this probability suggest about the accuracy of the test? 9) 10) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9). 10) 11) A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary. 11) 12) A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue). 12) Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 13) The following table contains data from a study of two airlines which fly to Small Town, USA. Number of flights Number of flights which were on time which were late Podunk Airlines 33 6 Upstate Airlines 43 5 If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time. 13) Answer the question. 14) What is the probability of an impossible event? 14) 15) Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected adolescents, where x is the number who are considered morbidly obese. Is it unusual to have no obese subjects among three randomly selected adolescents? x P(x) 0 0.111 1 0.215 2 0.450 3 0.224 15) Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 16) Rolling a single "loaded" die 11 times, keeping track of the "fives" rolled. 16) Use the given values of n and p to find the minimum usual value µ - 2 and the maximum usual value µ + 2. Round your answer to the nearest hundredth unless otherwise noted. 17) n = 1205, p = 0.98 17) 2
18) n = 753, p = 4 9 18) Solve the problem. 19) A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 11 questions on the survey? 19) 20) In a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure. 20) 21) How many ways can an IRS auditor select 3 of 9 tax returns for an audit? 21) 22) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed? 22) Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than µ - 2 or greater than µ + 2. 23) The Acme Candy Company claims that 8% of the jawbreakers it produces actually 23) result in a broken jaw. Suppose 9571 persons are selected at random from those who have eaten a jawbreaker produced at Acme Candy Company. Would it be unusual for this sample of 9571 to contain 801 persons with broken jaws? Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 24) n = 676; p = 0.7 24) Provide a written description of the complement of the given event. 25) When 100 engines are shipped, all of them are free of defects. 25) 26) Of the thirteen different women Calvin asks for a date, at least one of them accepts. 26) Identify the given random variable as being discrete or continuous. 27) The number of freshmen in the required course, English 101 27) 28) The ph level in a shampoo 28) 29) The number of oil spills occurring off the Alaskan coast 29) Evaluate the expression. 30) 8 P 4 30) Find the indicated probability. Round to three decimal places. 31) A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year? 31) 3
Find the indicated probability. Round to the nearest thousandth. 32) In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.1, what is the probability that the mixture will test positive? 32) Is Event B dependent or independent of Event A? 33) A: A Chicagoan visits New York on vacation. B: He visits Central Park. 33) 4
Answer Key Testname: STAT 50 REVIEW CHAPTERS 4&5 1) -$91.00 2) 0.472 3) 0.554 4) 0.324 5) 0.7 6) 0.267 7) 0.1390 8) 0.194 9) 0.103; The probability of this error is high so the test is not very accurate. 10) 2 13 11) 0.428 12) 7 10 13) 43 87 14) 0 15) No 16) Procedure results in a binomial distribution. 17) Minimum: 1171.18; maximum: 1190.62 18) Minimum: 307.4; maximum: 361.94 19) 39,916,800 20) 3.6 21) 84 22) 210 23) No 24) µ = 473.2 25) At least one of the engines is defective. 26) None of the women accept Calvin's offer. 27) Discrete 28) Continuous 29) Discrete 30) 1680 31) 0.126 32) 0.469 33) Dependent 5