MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Math1342: Statistics: Final Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. 1) You roll a six-sided die. Event B is rolling an even number. 1) A) 3; Simple event because the die is only rolled once. B) 2; Not a simple event because it is an event that consists of more than a single outcome. C)1; Simple event because it is an event that consists of a single outcome. D) 3; Not a simple event because it is an event that consists of more than a single outcome. 2) You randomly select a computer from a batch of 50 which contains 3 defective computers. Event B is selecting a defective computer. A) 1; Simple event because it is an event that consists of only one type of computer. B) 50; Not a simple event because it is an event that consists of more than a single outcome. C)3; Simple event because it is an event that consists of only one type of computer. D) 3; Not a simple event because it is an event that consists of more than a single outcome. 2) From the information provided, create the sample space of possible outcomes. 3) Flip a coin twice. A) HH HT TH TT B) HH TT HT HT C)HH HT TT D) HT TH 3) Determine whether the events are disjoint. 4) Draw one ball colored red from a bag. Draw one ball colored blue from the same bag. A) Yes B) No 4) Find the indicated complement. 5) The probability that Luis will pass his statistics test is Find the probability that he will fail his statistics test. A) 0.35 B) 0.74 C) 3.85 D) ) 6) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. A) B) C) 334 D) ) Find the indicated probability. 7) If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? A) 1 22 B) C) D) ) 1

2 8) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 9 wood 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) B) C) 0.57 D) There is insufficient information to answer the question. 8) 9) 100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time. 9) 1. Public transportation: 8 full time, 6 part time 2. Bicycle: 4 full time, 3 part time 3. Drive alone: 29 full time, 32 part time 4. Carpool: 8 full time, 10 part time A) 0.59 B) 0.67 C) 0.28 D) ) A 6-sided die is rolled. Find P(3 or 5). 10) A) 1 3 B) 2 C) 1 36 D) ) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9). A) 2 B) 8 C) 4 D) ) 12) A bag contains 6 red marbles, 2 blue marbles, and 1 green marble. Find P(not blue). 12) A) 7 9 B) 7 C) 2 9 D) ) The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Occasional smoker Regular smoker Heavy smoker Total Men Women Total ) If one of the 1081 people is randomly selected, find the probability of getting a regular or heavy smoker. A) B) C) D)

3 14) In one town, 20% 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. A) B) C) D) ) 15) When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, If a pair of dice are rolled 5 times, what is the probability of getting a sum of 5 every time? Round to eight decimal places. A) B) 0.04 C) D) ) 16) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction. A) 13 1 B) C) 25 D) , ) Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 17) The table below shows the soft drinks preferences of people in three age groups. cola root beer lemon-lime under 21 years of age between 21 and over 40 years of age ) If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age given that they drink root beer. A) 6 17 B) 2 5 C) 5 17 D) None of the above is correct. Evaluate the expression. 18) 12! 7! A) 2! B) 12 7 C) 95,040 D) 84,000 18) 19) 5 P 4 A) 24 B) 120 C)1 D) 5 19) 20) 8 C 3 A) 112 B) 120 C)56 D) 3 20) Solve the problem. 21) There are 13 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible? A) 120 B) 1287 C) 154,440 D) 371,293 21) 22) How many ways can an IRS auditor select 4 of 12 tax returns for an audit? A) 20,736 B) 24 C) 11,880 D) ) 3

4 23) 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? A) 210 B) 6 C)5 D) ) 24) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? A) 48 B) 720 C) 20,160 D) 40,320 24) 25) In a certain lottery, five different numbers between 1 and 31 inclusive are drawn. These are the winning numbers. To win the lottery, a person must select the correct 5 numbers in the same order in which they were drawn. What is the probability of winning? A) ,389,320 B) C) 1 31! D) 1 20,389,320 25) Use the fundamental counting principle to solve the problem. 26) A shirt company has 4 designs each of which can be made with short or long sleeves. There are 7 color patterns available. How many different shirts are available from this company? A) 28 B) 11 C)13 D) 56 26) 27) How many license plates can be made consisting of 2 letters followed by 3 digits? A) 676,000 B) 67,600 C) 11,881,376 D) 100,000 27) Find the mean of the given probability distribution. 28) The number of golf balls ordered by customers of a pro shop has the following probability distribution. x P(x) A) μ = 9 B) μ = 5.79 C)μ = 9.06 D) μ = ) 29) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.48, 0.39, 0.12, and 0.01, respectively. A) μ = 1.50 B) μ = 0.25 C)μ = 1.14 D) μ = ) Provide an appropriate response. Round to the nearest hundredth. 30) Find the standard deviation for the given probability distribution. x P(x) A) σ = 2.91 B) σ = 1.99 C)σ = 1.41 D) σ = ) 4

5 Provide an appropriate response. 31) In a game, you have a 1/27 probability of winning $100 and a 26/27 probability of losing $4. What is your expected value? A) -$3.85 B) $7.56 C) -$0.15 D) $ ) 32) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A) -$0.50 B) -$1.00 C) $0.00 D) -$ ) 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. 33) n = 4, x = 3, p = ) A) B) C) D) Find the indicated probability. Round to three decimal places. 34) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? A) B) C) D) ) Find the indicated probability. 35) An archer is able to hit the bull's-eye 50% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others. A) B) C) D) ) 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. 36) n = 2699; p = ) A) σ = B) σ = C)σ = D) σ = Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 37) n = 671; p = ) A) μ = B) μ = C)μ = D) μ = Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 38) 38) z A) B) C) D)

6 39) 39) z A) B) C) D) ) 40) z A) B) C) D) Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 41) Shaded area is ) z A) B) C) D) ) Shaded area is ) z A) B) 1.08 C) D) If z is a standard normal variable, find the probability. 43) The probability that z lies between 0 and 3.01 A) B) C) D) ) 44) The probability that z lies between 0.7 and 1.98 A) B) C) D) ) 45) P(z < 0.97) A) B) C) D) ) 6

7 Provide an appropriate response. 46) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of A) 91.0 B) 79.1 C) 82.3 D) ) Provide an appropriate response. Use the Standard Normal Table to find the probability. 47) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases? A) B) C) D) ) 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. 48) Between 8 pounds and 11 pounds 48) A) 2 3 B) 1 3 C) 1 4 D) 1 2 Solve the problem. 49) The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and a 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) B) C) D) ) Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 50) With n = 18 and p = 0.30, estimate P(6). 50) A) B) C) D) ) A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers. A) B) C) D) ) 52) Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective. A) B) C) D) ) Use the normal distribution to approximate the desired probability. 53) Find the probability that in 200 tosses of a fair die, we will obtain at least 30 fives. A) B) C) D) ) Find the percentile for the data value. 54) Data set: ; data value: 21 A) 60 B) 52 C)70 D) 35 54) Find the variance for the given data. Round your answer to one more decimal place than the original data. 55) A) 18.9 B) 15.2 C) 19.0 D) ) 7

8 Find the number of standard deviations from the mean. Round your answer to two decimal places. 56) The test scores on the Chapter 7 mathematics test have a mean of 66 and a standard deviation of 13. Andrea scored 89 on the test. How many standard deviations from the mean is that? A) 0.60 standard deviations below the mean B) 1.77 standard deviations below the mean C) 1.77 standard deviations above the mean D) 0.60 standard deviations above the mean 56) Provide an appropriate response. 57) The following frequency distribution analyzes the scores on a math test. Find the class boundaries of scores interval ) Scores Number of students A) 40.5, 58.5 B) 40.5, 59.5 C) 39.5, 58.5 D) 39.5, ) The frequency distribution below summarizes employee years of service for Alpha Corporation. Determine the width of each class. 58) Years of service Frequency A) 10 B) 4 C)5 D) 6 8

9 59) The scores on a recent statistics test are given in the frequency distribution below. Construct the corresponding relative frequency distribution. Round relative frequencies to the nearest hundredth of a percent if necessary. 59) Scores Frequency A) C) Relative Scores Frequency % % % % % Relative Scores Frequency % % % % % B) D) Relative Scores Frequency % % % % % Relative Scores Frequency % % % % % 60) The scores of the top ten finishers in a recent golf tournament are listed below. Find the median score. 60) A) 72 B) 67 C)71 D) 73 61) The scores of the top ten finishers in a recent golf tournament are listed below. Find the mode score. 61) A) 72 B) 73 C)76 D) 67 Approximate the mean of the grouped data. 62) Miles (per day) Frequency A) 4 B) 5 C)15 D) 6 62) 9

10 Provide an appropriate response. 63) Find the sample standard deviation. 63) A) 1.6 B) 4.8 C)2.8 D) 4.2 Use the grouped data formulas to find the indicated mean or standard deviation. 64) The salaries of a random sample of a company's employees are summarized in the frequency distribution below. Approximate the sample mean. 64) Salary ($) Employees 5,001-10, ,001-15, ,001-20, ,001-25, ,001-30, A) $17,500 B) $20, C) $16, D) $18, Provide an appropriate response. 65) The ages of 10 grooms at their first marriage are listed below. Find the midquartile. 65) A) 43.7 B) 34.1 C) 34.5 D) ) A teacher gives a 20-point quiz to 10 students. The scores are listed below. What percentile corresponds to the score of 12? 66) A) 25 B) 12 C)40 D) 13 Find the number of standard deviations from the mean. Round your answer to two decimal places. 67) The test scores on the Chapter 4 mathematics test have a mean of 70 and a standard deviation of 13. Andrea scored 92 on the test. How many standard deviations from the mean is that? A) 1.69 standard deviations above the mean B) 1.69 standard deviations below the mean C) 0.62 standard deviations above the mean D) 0.62 standard deviations below the mean 67) Find the percentile for the data value. 68) Data set: ; data value: 70 A) 70 B) 60 C)35 D) 52 68) Find the number of standard deviations from the mean. Round your answer to two decimal places. 69) The test scores on the Chapter 2 mathematics test have a mean of 64 and a standard deviation of 14. Andrea scored 93 on the test. How many standard deviations from the mean is that? A) 0.54 standard deviations below the mean B) 2.07 standard deviations above the mean C) 0.54 standard deviations above the mean D) 2.07 standard deviations below the mean 69) 10

11 Solve the problem. 70) A sample of 51 eggs yields a mean weight of 1.58 ounces. Assuming that σ = 0.58 ounces, find the margin of error in estimating μ at the 95% level of confidence. A) 0.43 oz B) 0.13 oz C)0.16 oz D) 0.02 oz 70) Find the necessary sample size. 71) Scores on a certain test are normally distributed with a variance of 100. A researcher wishes to estimate the mean score achieved by all adults on the test. Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 4 units. A) 25 B) 2401 C)97 D) 10 71) Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. 72) Systolic blood pressures for women aged 18-24: 94% confidence; n = 96, x = mm Hg, σ = 12.7 mm Hg A) 50.6 mm Hg B) 2.4 mm Hg C)2.0 mm Hg D) 2.2 mm Hg 72) Find the confidence interval specified. 73) A sample of 32 people were randomly selected from among the workers in a shoe factory. The time taken for each person to polish a finished shoe was measured. The sample mean was 3.1 minutes. Assume that σ = 0.94 minutes. Construct a 90% confidence interval for the true mean time, μ, to polish a shoe. A) 2.77 to 3.43 minutes B) 2.71 to 3.49 minutes C)2.83 to 3.37 minutes D) 2.67 to 3.53 minutes 73) Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. 74) Test scores: n = 104, x = 78.8, σ = 6.9; 99% confidence A) 77.1 < μ < 80.5 B) 77.5 < μ < 80.1 C)77.2 < μ < 80.4 D) 77.7 < μ < ) Use the given information to find the minimum sample size required to estimate an unknown population mean μ. 75) Margin of error: $139, confidence level: 95%, σ = $519 75) A) 76 B) 38 C)47 D) 54 A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical -value approach. 76) x = 20, n = 60, σ = 1.5, H0: μ = 22; Ha: μ 22, α = 0.05 A) z = ; critical values = ±1.645; reject H0 B) z = ; critical values = ±1.645; do not reject H0 C)z = ; critical values = ±1.96; do not reject H0 D) z = ; critical values = ±1.96; reject H0 76) 77) x = 51, n = 52, σ = 3.6, H0: μ = 50; Ha: μ > 50, α = 0.01 A) z = 0.28; critical value = 2.33; do not reject H0 B) z = 2.00; critical value = 1.33; reject H0 C)z = 2.00; critical value = 2.33; reject H0 D) z = 2.00; critical value = 2.33; do not reject H0 77) 11

12 Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. 78) The mean replacement time for a random sample of 20 washing machines is 9.2 years and the 78) standard deviation is 2.0 years. Construct a 99% confidence interval for the standard deviation, σ, of the replacement times of all washing machines of this type. A) 1.4 yr < σ < 3.3 yr B) 1.4 yr < σ < 3.8 yr C)1.4 yr < σ < 4.2 yr D) 1.4 yr < σ < 3.2 yr Provide an appropriate response. 79) Compute the standardized test statistic, X2 to test the claim σ if n = 10, s2 = 15, and α = A) B) C) D) ) Find the specified t-value. 80) For a t-curve with df = 6, find the two t-values that divide the area under the curve into a middle 0.99 area and two outside areas of A) , B) 0, C) 0, D) , ) Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of ) r = 0.41, n = 25 81) A) Critical values: r = ±0.487, no significant linear correlation B) Critical values: r = ±0.396, no significant linear correlation C) Critical values: r = ±0.396, significant linear correlation D) Critical values: r = ±0.487, significant linear correlation Find the value of the linear correlation coefficient r. 82) x y A) B) C) 0 D) ) Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. 83) x ) y A) y^ = 2.8x B) y^ = x C)y^ = 3.0x D) y^ = x 12

13 Find the value of the chi-square test statistic for the goodness-of-fit test. 84) The following table is obtained from a random sample of 30 absences. 84) Day Mon Tue Wed Thur Fri Number Absent You wish to test the claim that the absences occur on the five days with equal frequency. What is the value of the χ2 test statistic? The observed frequencies and the expected frequencies are shown below. Observed Frequency (O) Expected Frequency (E) A) χ2 = 9 B) χ2 = 3.6 C)χ2 = 6 D) χ2 = 4.5 Provide an appropriate response. 85) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic χ2 to test the claim that the number of wins is uniformly distributed across the different starting positions. The results are based on 240 wins. 85) Starting Position Number of Wins A) B) C) D)

14 Answer Key Testname: STATS-FINAL-REVIEW 1) D 2) D 3) A 4) A 5) B 6) C 7) C 8) C 9) A 10) A 11) A 12) A 13) B 14) C 15) C 16) C 17) B 18) C 19) B 20) C 21) B 22) D 23) A 24) C 25) D 26) D 27) A 28) D 29) D 30) C 31) C 32) A 33) B 34) B 35) D 36) A 37) C 38) A 39) A 40) B 41) B 42) D 43) C 44) D 45) B 46) D 47) A 48) D 49) B 50) B 14

15 Answer Key Testname: STATS-FINAL-REVIEW 51) C 52) A 53) D 54) A 55) C 56) C 57) D 58) C 59) B 60) A 61) A 62) B 63) B 64) D 65) D 66) C 67) A 68) B 69) B 70) C 71) A 72) B 73) C 74) A 75) D 76) D 77) D 78) A 79) B 80) D 81) C 82) A 83) C 84) C 85) B 15