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STATISTICS/GRACEY PRACTICE TEST/EXAM 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the indicated degree of likelihood as a probability value. 1) "There is a 40% chance of rain tomorrow." 1) A) 0.60 B) 0.40 C) 40 D) 4 2) "It will definitely turn dark tonight." 2) A) 0.30 B) 1 C) 0.5 D) 0.67 Answer the question. 3) Which of the following cannot be a probability? 3) 2 5 1 3 A) B) C) D) 3 3 2 5 4) What is the probability of an impossible event? 4) A) 1 B) -1 C) 0.1 D) 0 5) On a multiple choice test with four possible answers for each question, what is the probability of 5) answering a question correctly if you make a random guess? 1 3 1 A) B) C) D) 1 2 4 4 Find the indicated probability. 6) A die with 12 sides is rolled. What is the probability of rolling a number less than 11? 6) 1 11 5 A) B) C) 10 D) 12 12 6 7) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice 7) will be 5? 8 1 5 A) B) C) D) 4 9 9 6 8) The data set represents the income levels of the members of a country club. Find the probability 8) that a randomly selected member earns at least $88,000. Round your answers to the nearest tenth. 108,000 128,000 82,000 138,000 85,000 108,000 88,000 76,000 158,000 208,000 79,000 98,000 148,000 85,000 128,000 118,000 88,000 168,000 73,000 118,000 A) 0.8 B) 0.6 C) 0.4 D) 0.7 1 9) Refer to the table which summarizes the results of testing for a certain disease. 9) Positive Test Result Negative Test Result Subject has the disease 83 7 Subject does not have the disease 26 153 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? A) 0.0967; The probability of this error is high so the test is not very accurate. B) 0.405; The probability of this error is high so the test is not very accurate. C) 0.145; The probability of this error is high so the test is not very accurate. D) 0.0260; The probability of this error is low so the test is fairly accurate. Estimate the probability of the event. 10) A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, 10) obtained the set of survey responses to make its estimate. The encoding system for the data is: 0 = FOR, 1 = AGAINST. If the referendum were held today, estimate the probability that it would pass. 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0 A) 0.5 B) 0.65 C) 0.4 D) 0.6 11) Of 1936 people who came into a blood bank to give blood, 200 people had high blood pressure. 11) Estimate the probability that the next person who comes in to give blood will have high blood pressure. A) 0.022 B) 0.103 C) 0.071 D) 0.154 Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. 12) Is it "unusual" to get a 12 when a pair of dice is rolled? 12) A) Yes B) No 13) Is it "unusual" to get 7 when a pair of dice is rolled? 13) A) Yes B) No 14) Assume that a study of 500 randomly selected school bus routes showed that 477 arrived on time. 14) Is it "unusual" for a school bus to arrive late? A) Yes B) No 15) Assume that one student in your class of 23 students is randomly selected to win a prize. Would it 15) be "unusual" for you to win? A) Yes B) No From the information provided, create the sample space of possible outcomes. 16) Flip a coin three times. 16) A) HHH HTT HTH TTT HTT THH HHT THT B) HHH HHT HTH HTT THH THT TTH TTT C) HTT THT HTH HHH TTH TTT D) HHH TTT THT HTH HHT TTH HTH 2 17) Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each 17) takes out a piece and eats it. What are the possible pairs of candies eaten? A) CD-LD LD-LP LP-CD LP-LP LD-LD B) LD-LD CD-LD LP-LP LD-LP CD-CD LD-LP LP-CD CD-LD LP-LD C) LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD CD-LP LP-LD D) LD-CD LD-CD LD-CD LD-LP LD-LP LD-LP CD-LP CD-LP CD-LP Answer the question. 18) Find the odds against correctly guessing the answer to a multiple choice question with 7 possible 18) answers. A) 6 : 1 B) 6 : 7 C) 7 : 6 D) 7 : 1 19) Suppose you are playing a game of chance. If you bet $6 on a certain event, you will collect $174 19) (including your $6 bet) if you win. Find the odds used for determining the payoff. A) 174 : 180 B) 1 : 28 C) 29 : 1 D) 28 : 1 Determine whether the events are disjoint. 20) Draw one ball colored red from a bag. 20) Draw one ball colored blue from the same bag. A) Yes B) No 21) Meet a man with an umbrella. 21) Meet a man with a raincoat. A) Yes B) No 22) Get a full time day job as a teller with a bank. 22) Get a full time day job as a cashier at a store. A) Yes B) No Find the indicated complement. 15 23) If P(A) = , find P(A). 23) 17 17 15 2 A) B) C) D) 0 15 32 17 24) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore 24) leap years. 31 11 31 334 A) B) C) D) 365 12 334 365 Find the indicated probability. 25) A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will 25) stop on an even number or a multiple of 3? 1 2 7 A) B) C) 12 D) 3 3 9 3 26) The table below describes the smoking habits of a group of asthma sufferers. 26) Occasional Regular Heavy Nonsmoker smoker smoker smoker Total Men 389 36 83 37 545 Women 419 36 89 35 579 Total 808 72 172 72 1124 If one of the 1124 people is randomly selected, find the probability that the person is a man or a heavy smoker. A) 0.516 B) 0.514 C) 0.483 D) 0.549 27) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 9 wood 27) and 14 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective. A) 0.115 B) 0.545 C) 0.57 D) There is insufficient information to answer the question. 28) A study of consumer smoking habits includes 175 people in the 18-22 age bracket (42 of whom 28) smoke), 136 people in the 23-30 age bracket (40 of whom smoke), and 96 people in the 31-40 age bracket (26 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. A) 0.294 B) 0.6 C) 0.501 D) 0.098 29) The manager of a bank recorded the amount of time each customer spent waiting in line during 29) peak business hours one Monday. The frequency table below summarizes the results. Waiting Time Number of (minutes) Customers 0-3 11 4-7 11 8-11 10 12-15 6 16-19 4 20-23 2 24-27 2 If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes? A) 0.13 B) 0.652 C) 0.522 D) 0.727 30) A 6-sided die is rolled. Find P(3 or 5). 30) 1 1 1 A) B) C) D) 2 6 36 3 31) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4). 31) 2 4 12 A) 16 B) C) D) 13 13 13 4 32) A bag contains 6 red marbles, 2 blue marbles, and 1 green marble. Find P(not blue). 32) 7 2 9 A) B) 7 C) D) 9 9 7 Is Event B dependent or independent of Event A? 33) A: A mosquito lands on your arm. 33) B: You get a mosquito bite. A) Dependent B) Independent 34) A: A bird lands on your head. 34) B: The bird lays an egg. A) Independent B) Dependent Find the indicated probability. 35) In one town, 20% of all voters are Democrats. If two voters are randomly selected for a survey, find 35) the probability that they are both Democrats. Round to the nearest thousandth if necessary. A) 0.038 B) 0.040 C) 0.400 D) 0.200 36) Find the probability of correctly answering the first 2 questions on a multiple choice test if random 36) guesses are made and each question has 5 possible answers. 5 1 2 1 A) B) C) D) 2 32 5 25 37) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good 37) coils when two coils are randomly selected if the first selection is replaced before the second is made. A) 0.7733 B) 0.7744 C) 0.0144 D) 0.176 38) When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of 38) dice are rolled 5 times, what is the probability of getting a sum of 5 every time? Round to eight decimal places. A) 0.00005168 B) 0.00032 C) 0.00001694 D) 0.04 39) A study conducted at a certain college shows that 61% of the school's graduates find a job in their 39) chosen field within a year after graduation. Find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating. Round to the nearest thousandth if necessary. A) 0.082 B) 3.050 C) 0.138 D) 0.084 40) In a homicide case 7 different witnesses picked the same man from a line up. The line up contained 40) 5 men. If the identifications were made by random guesses, find the probability that all 7 witnesses would pick the same person. A) 0.000064 B) 1.4 C) 0.0000595 D) 0.0000128 41) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing 41) cards. Find the probability that both cards are black. Express your answer as a simplified fraction. 25 25 13 1 A) B) C) D) 102 51 51 2,652 5 42) A IRS auditor randomly selects 3 tax returns from 55 returns of which 6 contain errors. What is the 42) probability that she selects none of those containing errors? Round to four decimal places. A) 0.0008 B) 0.7023 C) 0.0013 D) 0.7071 43) The table below describes the smoking habits of a group of asthma sufferers. 43) Light Heavy Nonsmoker smoker smoker Total Men 402 35 42 479 Women 376 45 33 454 Total 778 80 75 933 If two different people are randomly selected from the 933 subjects, find the probability that they are both heavy smokers. Round to six decimal places. A) 0.006383 B) 0.006462 C) 0.002026 D) 0.0001778 Provide a written description of the complement of the given event. 44) Of ten adults, at least one of them has high blood pressure. 44) A) Nine of the adults have high blood pressure. B) None of the adults have high blood pressure. C) All of the adults have high blood pressure. D) At most one of the adults has high blood pressure. 45) When several textbooks are edited, none of them are found to be free of errors. 45) A) At least one of the textbooks is free of errors. B) One of the textbooks is free of errors. C) All of the textbooks are free of errors. D) At most one of the textbooks is free of errors. Find the indicated probability. Round to the nearest thousandth. 46) An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the 46) probability that there is at least one correct answer. A) 0.900 B) 0.999 C) 0.100 D) 0.001 47) A study conducted at a certain college shows that 59% of the school's graduates find a job in their 47) chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. A) 0.590 B) 0.167 C) 0.995 D) 0.958 48) In a blood testing procedure, blood samples from 3 people are combined into one mixture. The 48) 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? A) 0.729 B) 0.999 C) 0.00100 D) 0.271 6 Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 49) The table below shows the soft drinks preferences of people in three age groups. 49) cola root beer lemon-lime under 21 years of age 40 25 20 between 21 and 40 35 20 30 over 40 years of age 20 30 35 If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age. 3 1 2 1 A) B) C) D) 5 2 5 3 50) The following table contains data from a study of two airlines which fly to Small Town, USA. 50) 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 arrived on time. 76 11 A) B) 87 76 43 C) D) None of the above is correct. 87 Evaluate the expression. 12! 51) 51) 7! 12 A) 95,040 B) 84,000 C) 2! D) 7 52) 8 P4 52) A) 4 B) 70 C) 2 D) 1680 53) 8 C3 53) A) 3 B) 120 C) 56 D) 112 Solve the problem. 54) There are 13 members on a board of directors. If they must form a subcommittee of 5 members, 54) how many different subcommittees are possible? A) 120 B) 371,293 C) 154,440 D) 1287 55) How many ways can an IRS auditor select 4 of 12 tax returns for an audit? 55) A) 20,736 B) 11,880 C) 24 D) 495 7 56) A state lottery involves the random selection of six different numbers between 1 and 28. If you 56) select one six number combination, what is the probability that it will be the winning combination? 1 1 1 1 A) B) C) D) 376,740 720 271,252,800 481,890,304 57) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is 57) not allowed? A) 5 B) 6 C) 210 D) 343 58) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to 58) choose from? A) 48 B) 20,160 C) 40,320 D) 720 59) A musician plans to perform 7 selections. In how many ways can she arrange the musical 59) selections? A) 7 B) 5040 C) 40,320 D) 49 60) A tourist in France wants to visit 5 different cities. If the route is randomly selected, what is the 60) probability that she will visit the cities in alphabetical order? 1 1 1 A) B) C) 120 D) 25 120 5 Answer the question. 61) If you are told that a randomly selected mystery person was born in the 1990's, what is the 61) probability of guessing his/her exact birth date (including year)? A) 2.738 × 10-3 B) 2.740 × 10-4 C) 2.737 × 10-3 D) 2.738 × 10-4 62) 12 wrestlers compete in a competition. If each wrestler wrestles one match with each other 62) wrestler, what are the total numbers of matches? A) 78 B) 66 C) 132 D) 156 Identify the given random variable as being discrete or continuous. 63) The number of oil spills occurring off the Alaskan coast 63) A) Discrete B) Continuous 64) The cost of a randomly selected orange 64) A) Discrete B) Continuous 65) The pH level in a shampoo 65) A) Discrete B) Continuous 66) The braking time of a car 66) A) Continuous B) Discrete 8 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. 67) 67) x P(x) 0 0.079 1 0.173 2 -0.030 3 0.170 4 0.075 5 0.533 68) A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be 68) reported in a given day are 0.135, 0.271, 0.271, 0.180, and 0.090, respectively. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean of the given probability distribution. 69) 69) x P(x) 0 0.14 1 0.10 2 0.25 3 0.25 4 0.26 A) μ = 2.29 B) μ = 2.53 C) μ = 2.39 D) μ = 2.43 70) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a 70) given day are 0.48, 0.39, 0.12, and 0.01, respectively. A) μ = 0.66 B) μ = 0.25 C) μ = 1.50 D) μ = 1.14 Provide an appropriate response. Round to the nearest hundredth. 71) Find the standard deviation for the given probability distribution. 71) x P(x) 0 0.12 1 0.17 2 0.09 3 0.28 4 0.34 A) σ = 2.91 B) σ = 1.45 C) σ = 1.99 D) σ = 1.41 72) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 72) 0.4979, 0.3793, 0.1084, 0.0138, and 0.0007, respectively. Find the standard deviation for the probability distribution. A) σ = 0.54 B) σ = 0.73 C) σ = 0.97 D) σ = 0.68 9 Answer the question. 73) Focus groups of 14 people are randomly selected to discuss products of the Yummy Company. It is 73) determined that the mean number (per group) who recognize the Yummy brand name is 10.9, and the standard deviation is 0.98. Would it be unusual to randomly select 14 people and find that fewer than 7 recognize the Yummy brand name? A) Yes B) No 74) Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 74) probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven games. Is it unusual for a team to win a series in 4 games? A) Yes B) No 75) Suppose that a law enforcement group studying traffic violations determines that the 75) accompanying table describes the probability distribution for five randomly selected people, where x is the number that have received a speeding ticket in the last 2 years. Is it unusual to find five speeders among five randomly selected people? x P(x) 0 0.08 1 0.18 2 0.25 3 0.22 4 0.19 5 0.08 A) Yes B) No Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x(girls) P(x) x(girls) P(x) x(girls) P(x) 0 0.000 5 0.122 10 0.061 1 0.001 6 0.183 11 0.022 2 0.006 7 0.209 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 76) Find the probability of selecting exactly 8 girls. 76) A) 0.000 B) 0.122 C) 0.183 D) 0.022 77) Find the probability of selecting 9 or more girls. 77) A) 0.001 B) 0.061 C) 0.212 D) 0.122 78) Find the probability of selecting 2 or more girls. 78) A) 0.999 B) 0.006 C) 0.001 D) 0.994 10 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 79) Let the random variable x represent the number of girls in a family of three children. 79) Construct a table describing the probability distribution, then find the mean and standard deviation. 80) Ten apples, four of which are rotten, are in a refrigerator. Three apples are randomly 80) selected without replacement. Let the random variable x represent the number chosen that are rotten. Construct a table describing the probability distribution, then find the mean and standard deviation for the random variable x. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 81) In a game, you have a 1/27 probability of winning $100 and a 26/27 probability of losing $4. What is 81) your expected value? A) -$0.15 B) -$3.85 C) $3.70 D) $7.56 82) Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for 82) rolling a 2 or a 4, nothing otherwise. What is your expected value? A) -$0.67 B) $2.00 C) -$2.00 D) $4.00 83) A 28-year-old man pays $200 for a one-year life insurance policy with coverage of $120,000. If the 83) probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? A) -$199.88 B) $119,928.00 C) -$128.00 D) $72.00 84) The prizes that can be won in a sweepstakes are listed below together with the chances of winning 84) each one: $3800 (1 chance in 8600); $1700 (1 chance in 5400); $700 (1 chance in 4600); $200 (1 chance in 2600). Find the expected value of the amount won for one entry if the cost of entering is 55 cents. A) $200 B) $0.44 C) $0.47 D) $0.91 Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 85) Rolling a single die 37 times, keeping track of the numbers that are rolled. 85) A) Not binomial: there are too many trials. B) Not binomial: there are more than two outcomes for each trial. C) Procedure results in a binomial distribution. D) Not binomial: the trials are not independent. 86) Rolling a single die 19 times, keeping track of the "fives" rolled. 86) A) Procedure results in a binomial distribution. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: there are too many trials. D) Not binomial: the trials are not independent. 11 87) Choosing 7 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time without 87) replacement, keeping track of the number of red marbles chosen. A) Not binomial: the trials are not independent. B) Not binomial: there are more than two outcomes for each trial. C) Procedure results in a binomial distribution. D) Not binomial: there are too many trials. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 88) Multiple-choice questions on a test each have 4 possible answers, one of which is correct. 88) Assume that you guess the answers to 4 such questions. a. Use the multiplication rule to find the probability that the first two guesses are wrong and the third and fourth guesses are correct. That is, find P(WWCC), where C denotes a correct answer and W denotes a wrong answer. b. Make a complete list of the different possible arrangements of 2 wrong answers and 2 correct answers, then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly 2 correct answers when 4 guesses are made? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. 1 89) n = 4, x = 3, p = 89) 6 A) 0.023 B) 0.004 C) 0.015 D) 0.012 90) n =12, x = 5, p = 0.25 90) A) 0.082 B) 0.103 C) 0.027 D) 0.091 Find the indicated probability. Round to three decimal places. 91) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions 91) correctly. If a student guesses on each question, what is the probability that the student will pass the test? A) 0.205 B) 0.377 C) 0.828 D) 0.172 92) A machine has 12 identical components which function independently. The probability that a 92) component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. A) 0.795 B) 0.927 C) 0.206 D) 0.133 93) An airline estimates that 90% of people booked on their flights actually show up. If the airline 93) books 71 people on a flight for which the maximum number is 69, what is the probability that the number of people who show up will exceed the capacity of the plane? A) 0.001 B) 0.005 C) 0.004 D) 0.022 12 94) A car insurance company has determined that 9% of all drivers were involved in a car accident last 94) year. Among the 11 drivers living on one particular street, 3 were involved in a car accident last year. If 11 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year? A) 0.057 B) 0.943 C) 0.424 D) 0.070 Find the indicated probability. 95) The brand name of a certain chain of coffee shops has a 49% recognition rate in the town of 95) 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 9 Coffleton residents. Find the probability that exactly 4 of the 9 Coffleton residents recognize the brand name. A) 0.00199 B) 0.0576 C) 0.174 D) 0.251 96) In a survey of 300 college graduates, 58% reported that they entered a profession closely related to 96) their college major. If 6 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major? A) 0.289 B) 0.157 C) 0.711 D) 0.195 97) The brand name of a certain chain of coffee shops has a 45% recognition rate in the town of 97) 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 9 Coffleton residents. Find the probability that exactly 4 of the 9 Coffleton residents recognize the brand name. A) 0.0410 B) 0.260 C) 0.00206 D) 0.212 98) A slot machine at a hotel is configured so that there is a 1/1600 probability of winning the jackpot 98) on any individual trial. If a guest plays the slot machine 5 times, find the probability of exactly 2 jackpots. If a guest told the hotel manager that she had hit two jackpots in 5 plays of the slot machine, would the manager be surprised? A) 0.000000391; Yes, the probability of 2 jackpots in 5 plays is extremely small. B) 0.00000390; Yes, the probability of 2 jackpots in 5 plays is extremely small. C) 0.000000390; Yes, the probability of 2 jackpots in 5 plays is extremely small. D) 0.0941; No, hitting 2 jackpots in 5 trials is not so unlikely. Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 99) n = 36; p = 0.2 99) A) μ = 7.2 B) μ = 7.9 C) μ = 6.7 D) μ = 7.5 100) n = 22; p = 3/5 100) A) μ = 13.5 B) μ = 13.2 C) μ = 12.7 D) μ = 13.9 Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. 101) n = 2699; p = 0.63 101) A) σ = 25.08 B) σ = 29.20 C) σ = 22.67 D) σ = 28.35 13 Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ. Round your answer to the nearest hundredth unless otherwise noted. 102) n = 93, p = 0.25 102) A) Minimum: -11.62; maximum: 58.13 B) Minimum: 31.6; maximum: 14.9 C) Minimum: 19.07; maximum: 27.43 D) Minimum: 14.9; maximum: 31.6 2 103) n = 351, p = 103) 7 A) Minimum: 88.32; maximum: 112.26 B) Minimum: 83.36; maximum: 117.21 C) Minimum: 91.82; maximum: 108.75 D) Minimum: 117.21; maximum: 83.36 104) n = 319, p = 0.243 Round your answers to the nearest thousandth. 104) A) Minimum: 66.684; maximum: 88.35 B) Minimum: 92.838; maximum: 62.196 C) Minimum: 69.857; maximum: 85.177 D) Minimum: 62.196; maximum: 92.838 Solve the problem. 105) According to a college survey, 22% of all students work full time. Find the mean for the number of 105) students who work full time in samples of size 16. A) 0.2 B) 2.8 C) 3.5 D) 4.0 106) A die is rolled 10 times and the number of times that two shows on the upper face is counted. If this 106) experiment is repeated many times, find the mean for the number of twos. A) 8.33 B) 2.5 C) 1.67 D) 3.33 107) On a multiple choice test with 9 questions, each question has four possible answers, one of which is 107) correct. For students who guess at all answers, find the mean for the number of correct answers. A) 4.5 B) 3 C) 2.3 D) 6.8 1 108) The probability of winning a certain lottery is . For people who play 746 times, find the 108) 67,158 mean number of wins. A) 0.0013 B) 0.0111 C) 0.000015 D) 90.0 109) A company manufactures batteries in batches of 19 and there is a 3% rate of defects. Find the 109) variance for the number of defects per batch. A) 55.3 B) 0.7 C) 0.6 D) 0.3 110) A die is rolled 17 times and the number of twos that come up is tallied. If this experiment is 110) repeated many times, find the standard deviation for the number of twos. A) 14.2 B) 4.3 C) 1.5 D) 2.1 111) In a certain town, 53% of voters favor a given ballot measure. For groups of 26 voters, find the 111) variance for the number who favor the measure. A) 6.5 B) 41.9 C) 13.8 D) 2.5 14 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 - 2σ or greater than μ + 2σ. 112) A survey for brand recognition is done and it is determined that 68% of consumers have heard of 112) Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 595 consumers who recognize the Dull Computer Company name? A) Yes B) No 113) The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 113) ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 544 jawbreakers that weigh more than .4 ounces? A) Yes B) No Using the following uniform density curve, answer the question. 114) What is the probability that the random variable has a value greater than 4? 114) A) 0.450 B) 0.375 C) 0.500 D) 0.625 115) What is the probability that the random variable has a value less than 4? 115) A) 0.250 B) 0.375 C) 0.625 D) 0.500 116) What is the probability that the random variable has a value between 0.2 and 0.8? 116) A) 0.2 B) 0.075 C) 0.05 D) 0.325 Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost. 117) More than 10 pounds 117) 2 1 1 5 A) B) C) D) 3 3 7 6 118) Between 8.5 pounds and 10 pounds 118) 3 1 1 1 A) B) C) D) 4 3 2 4 15 Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 119) 119) -3.39 -2.26 -1.13 1.13 2.26 3.39 z A) 0.8708 B) 0.8907 C) 0.1292 D) 0.8485 120) 120) -1.88 1.88 z A) 0.9398 B) 0.0301 C) 0.0602 D) 0.9699 Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 121) Shaded area is 0.9599. 121) z A) 1.03 B) -1.38 C) 1.75 D) 1.82 122) Shaded area is 0.0901. 122) z A) -1.39 B) -1.45 C) -1.34 D) -1.26 123) Shaded area is 0.8599. 123) z A) 0.8051 B) -1.08 C) 0.5557 D) 1.08 16 If z is a standard normal variable, find the probability. 124) The probability that z lies between 0 and 3.01 124) A) 0.4987 B) 0.9987 C) 0.5013 D) 0.1217 125) The probability that z lies between -2.41 and 0 125) A) 0.0948 B) 0.5080 C) 0.4910 D) 0.4920 126) The probability that z is less than 1.13 126) A) 0.1292 B) 0.8485 C) 0.8708 D) 0.8907 127) The probability that z lies between -1.10 and -0.36 127) A) 0.2239 B) -0.2237 C) 0.4951 D) 0.2237 128) The probability that z lies between 0.7 and 1.98 128) A) 0.2181 B) 0.2175 C) 1.7341 D) -0.2181 129) The probability that z lies between -0.55 and 0.55 129) A) -0.4176 B) -0.9000 C) 0.9000 D) 0.4176 130) P(z > 0.59) 130) A) 0.2224 B) 0.7224 C) 0.2190 D) 0.2776 131) P(-0.73 < z < 2.27) 131) A) 0.2211 B) 0.7557 C) 0.4884 D) 1.54 The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. 132) Find P96, the 96th percentile. 132) A) -1.38° B) 1.75° C) 1.03° D) 1.82° 133) Find Q3 , the third quartile. 133) A) 0.53° B) 0.82° C) 0.67° D) -1.3° 134) If 7% of the thermometers are rejected because they have readings that are too high, but all other 134) thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. A) 1.48° B) 1.26° C) 1.45° D) 1.39° 135) A quality control analyst wants to examine thermometers that give readings in the bottom 4%. Find 135) the reading that separates the bottom 4% from the others. A) -1.89° B) -1.63° C) -1.75° D) -1.48° Find the indicated value. 136) z 0.05 136) A) 1.645 B) 1.755 C) 1.325 D) 1.545 17 137) z 0.36 137) A) 0.36 B) 0.45 C) 1.76 D) 1.60 Provide an appropriate response. 138) Which of the following is true about the distribution of IQ scores? 138) A) The median is 100. B) The standard deviation is 20. C) The mean is 1. D) The mean is 75. 139) Which of the following is true about the distribution of IQ scores? 139) A) The area under its bell-shaped curve is 1. B) The area under its bell-shaped curve is 10. C) The area under its bell-shaped curve is 2. D) Its distribution is skewed to the right. 140) Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are 140) normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). A) 0.7619 B) 0.7303 C) 0.7745 D) 0.7938 141) Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally 141) distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). The shaded area under the curve is 0.5675. A) 102.6 B) 110.7 C) 97.5 D) 129.6 142) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard 142) deviation of 15 (as on the Wechsler test). Find the probability that a randomly selected adult has an IQ between 90 and 120 (somewhere in the range of normal to bright normal). A) 0.6568 B) 0.6014 C) 0.6977 D) 0.6227 Solve the problem. Round to the nearest tenth unless indicated otherwise. 143) Scores on a test are normally distributed with a mean of 67.7 and a standard deviation of 9.3. Find 143) P81, which separates the bottom 81% from the top 19%. A) 0.88 B) 75.9 C) 0.291 D) 70.4 18 144) Human body temperatures are normally distributed with a mean of 98.20°F and a standard 144) deviation of 0.62°F. Find the temperature that separates the top 7% from the bottom 93%. Round to the nearest hundredth of a degree. A) 98.78°F B) 97.28°F C) 99.12°F D) 98.40°F Assume that X has a normal distribution, and find the indicated probability. 145) The mean is μ = 60.0 and the standard deviation is σ = 4.0. 145) Find the probability that X is less than 53.0. A) 0.0802 B) 0.9599 C) 0.5589 D) 0.0401 146) The mean is μ= 15.2 and the standard deviation is σ = 0.9. 146) Find the probability that X is greater than 16.1. A) 0.1357 B) 0.8413 C) 0.1550 D) 0.1587 147) The mean is μ = 137.0 and the standard deviation is σ = 5.3. 147) Find the probability that X is between 134.4 and 140.1. A) 0.4069 B) 0.8138 C) 1.0311 D) 0.6242 Find the indicated probability. 148) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 148) inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? A) 47.72% B) 2.28% C) 97.72% D) 37.45% 149) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a 149) standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week? A) 0.2823 B) 0.7823 C) 0.2177 D) 0.1003 150) The lengths of human pregnancies are normally distributed with a mean of 268 days and a 150) standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days? A) 0.0166 B) 0.0179 C) 0.9834 D) 0.4834 Solve the problem. 151) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 151) 91 inches, and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 93.8 inches? A) 0.4192 B) 0.5808 C) 0.0808 D) 0.0026 152) The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and a 152) standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 8.6 and 14.6 lb? A) 0.3270 B) 0.6730 C) 0.0968 D) 0.4032 153) The scores on a certain test are normally distributed with a mean score of 60 and a standard 153) deviation of 2. What is the probability that a sample of 90 students will have a mean score of at least 60.2108? A) 0.8413 B) 0.3174 C) 0.1587 D) 0.3413 19 154) Human body temperatures are normally distributed with a mean of 98.20°F and a standard 154) deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F. A) 0.0833 B) 0.9826 C) 0.3343 D) 0.4826 155) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet 155) Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours. A) 0.1346 B) 0.1946 C) 0.1469 D) 0.1285 156) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet 156) Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours. A) 0.0103 B) 0.0036 C) 0.0025 D) 0.0008 157) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly 157) selected, find the probability that the mean of their test scores is greater than 78. A) 0.0036 B) 0.8962 C) 0.0008 D) 0.0103 158) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly 158) selected, find the probability that the mean of their test scores is less than 76. A) 0.9699 B) 0.9203 C) 0.0301 D) 0.8962 20 Answer Key Testname: PRACTICE EXAM 2 1) B 2) B 3) B 4) D 5) C 6) D 7) B 8) D 9) A 10) D 11) B 12) A 13) B 14) A 15) A 16) B 17) C 18) A 19) D 20) A 21) B 22) A 23) C 24) D 25) B 26) A 27) C 28) C 29) C 30) C 31) C 32) A 33) A 34) A 35) B 36) D 37) B 38) C 39) D 40) A 41) A 42) B 43) A 44) B 45) A 46) B 47) C 48) D 49) D 50) A 21 Answer Key Testname: PRACTICE EXAM 2 51) A 52) D 53) C 54) D 55) D 56) A 57) C 58) B 59) B 60) B 61) D 62) B 63) A 64) A 65) B 66) A 67) Not a probability distribution. One of the P(x)'s is negative. 68) Not a probability distribution. The sum of the P(x)'s is not 1, since 0.9470 ≠ 1.0000. 69) C 70) A 71) D 72) B 73) A 74) A 75) B 76) C 77) C 78) A 79) x P(x) 0 0.125 1 0.375 2 0.375 3 0.125 μ = 1.500 σ = 0.866 80) x P(x) 0 0.167 1 0.500 2 0.300 3 0.033 μ = 1.200 σ = 0.748 81) A 82) A 83) C 84) B 85) B 86) A 22 Answer Key Testname: PRACTICE EXAM 2 87) A 88) a. 0.0352 b. WWCC WCWC WCCW CWWC CWCW CCWW Each of the 6 arrangements has probability 0.0352 c. 0.211 89) C 90) B 91) B 92) A 93) B 94) D 95) D 96) A 97) B 98) B 99) A 100) B 101) A 102) D 103) B 104) D 105) C 106) C 107) C 108) B 109) C 110) C 111) A 112) A 113) A 114) C 115) D 116) B 117) B 118) D 119) A 120) A 121) C 122) C 123) B 124) A 125) D 126) C 127) D 128) A 23 Answer Key Testname: PRACTICE EXAM 2 129) D 130) D 131) B 132) B 133) C 134) A 135) C 136) A 137) A 138) A 139) A 140) D 141) A 142) A 143) B 144) C 145) D 146) D 147) A 148) B 149) C 150) A 151) C 152) B 153) C 154) B 155) C 156) C 157) C 158) A 24