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Math 160 Midterm Review Multiple Choice: Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response 1. The following frequency distribution analyzes the scores on a math test. Find the class boundaries of scores interval 40 – 59. Scores 40-59 60-75 76-82 83-94 95-99 A. B. C. D. Number of Students 2 4 6 15 5 39.5, 58.5 40.5, 59.5 39.5, 59.5 40.5, 58.5 2. The frequency distribution below summarizes employee years of service for Alpha Corporation. Determine the width of each class. Years of Service 1-5 6-10 11-15 16-20 21-25 26-30 A. B. C. D. 6 4 5 10 Frequency 5 20 25 10 5 3 3. The frequency distribution for the weekly incomes of students with part-time jobs is given below. Construct the corresponding relative frequency distribution. Round relative frequencies to the nearest hundredth of a percent if necessary. Income ($) 200-300 301-400 401-500 501-600 More than 600 Frequency 60 73 91 89 15 A. Income ($) 200-300 301-400 401-500 501-600 More than 600 Relative Frequency 18.29% 22.26% 27.74% 27.13% 4.57% B. Income ($) 200-300 301-400 401-500 501-600 More than 600 Relative Frequency 12.5% 20.1% 37.3% 15.2% 14.9% C. Income ($) 200-300 301-400 401-500 501-600 More than 600 Relative Frequency 15.5% 22.1% 31.3% 16.2% 14.9% D. Income ($) 200-300 301-400 Relative Frequency 27.33% 27.38% Income ($) 401-500 501-600 More than 600 Relative Frequency 4.60% 18.07% 27.41% 4. A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. The blood pressure readings were given to the nearest whole number. Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading between 110 and 139 inclusive? A. B. C. D. 75% 89% 39% 59% 5. In a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are shown below. Construct a histogram to represent the data. Use 4 classes with a class width of 10, and begin with a lower class limit of -0.5. What is the approximate amount at the center? 6, 15, 3, 36, 25, 18, 12, 18, 5, 30, 24, 7, 0, 22, 33, 24, 19, 4, 12, 9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the original data from the stem plot 6. Stem 9 10 11 A. B. C. D. Leaves 59 19 55 95, 91, 99, 101, 111, 115 95, 99, 101, 109, 115, 115 95, 99, 101, 101, 115, 115 91, 95, 91, 109, 119, 115 Construct a pie chart representing the given data set. 7. The following data give the distribution of the types of houses in a town containing 44,000 houses. Capes – 11,000 Garrisons – 15,400 Splits – 17,699 Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. 8. Andrew asked seven of his friends how many cousins they had. The results are listed below. Find the mean number of cousins. 18, 12, 7, 13, 7, 2, 7 A. B. C. D. 9.4 Cousins 11 cousins 10.9 cousins 8.9 cousins Find the median for the given sample data 9. The distances (in miles) driven in the past week by each of a company's sales representatives are listed below. 107, 114, 214, 230, 436, 445 Find the Media Distance driven: A. B. C. D. 222 mi 220.50 mi 230 mi 214 mi Find the mode(s) for the given sample data 10. Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. 53, 65, 63, 50, 56, 67, 62, 58, 54 A. B. C. D. 53 yr, 65 yr, 63 yr, 50 yr, 56 yr, 67 yr, 62 yr, 58 yr, 54 yr. 58 yr 58.7 yr No mode Find the midrange for the given sample data 11. A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities. The results are shown below. Find the midrange. 72, 143, 52, 84, 100, 98, 101, 120, 99, 121, 86, 60, 59, 71, 125, 130, 104, 74, 83, 55, 169 A. B. C. D. 110.5 days 117 days 112 days 98 days Find the mean of the data summarized in the given frequency distribution 12. The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. Speed (mph) 30-39 Cars 4 Speed (mph) 40-49 50-59 60-69 70-79 A. B. C. D. Cars 19 50 15 12 61.3 mph 58.5 mph 55.7 mph 54.5 mph Find the range for the given sample data. 13. Jorge has his own business as a painter. The amounts he made in the last five months are shown below. $2416, $2423, $1644, $2036, $1267 A. B. C. D. $1149 $1156 $779 $772 Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 14. Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores: 50, 15, 31, 27, 11, 42, 71 A. B. C. D. 11,341 31 20.9 8715.6 Find the standard deviation of the data summarized in the given frequency distribution. 15. A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation. Salary (dollars) 5001- 10000 10001 – 15000 Employees 12 13 A. B. C. D. Salary (dollars) 15001 – 20000 20001 – 25000 25001 – 30000 $7674.1 $7461.0 $7105.7 $7887.3 Employees 14 19 22 Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. 16. The race speeds for the top eight cars in a 200-rnile race are listed below. 185.9, 179.5, 189.2, 176.7, 175.6, 188.7, 186.3, 177.9 A. B. C. D. 1.1 7.5 6.8 3.4 Use the empirical rule to solve the problem. 17. At one college, GP A's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. What percentage of students at the college have a GP A between 2.3 and 3.5? A. B. C. D. 84.13% 68% 99.7% 95% Solve the problem. Round results to the nearest hundredth. 18. The mean height of a basketball team is 6 feet with a standard deviation of 0.2 feet. The team's center is 6.7 feet tall. Find the center's z score. Is his score unusual? A. B. C. D. 2.98, no 3, no 3.5, yes 3.85, yes Find the number of standard deviations from the mean. Round your answer to two decimal places. 19. The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10 inches. Last year there were 63 inches of snow. How many standard deviations from the mean is that? A. B. C. D. 0.44 standard deviations above the mean 2.50 standard deviations below the mean 0.44 standard deviations below the mean 2.50 standard deviations above the mean Determine which score corresponds to the higher relative position. 20. Which is better: a score of 82 on a test with a mean of 70 and a standard deviation of 8, or a score of 82 on a test with a mean of 75 and a standard deviation of 4? A. The first 82 B. The second 82 C. Both scores have the same relative position Find the percentile for the data value. 21. Date set: 4, 6, 14, 10, 4, 10, 18, 18, 22, 6, 6, 18, 12, 2, 18; Data value: 14 A. B. C. D. 52 35 60 70 Find the indicated measure. 22. The test scores of 40 students are listed below. Find P56. 30, 35, 43, 44, 47, 48, 54, 55, 56, 57, 59, 62, 63, 65, 66, 68, 69, 71, 72, 72, 73, 74, 76, 77, 77, 78, 79, 80, 81, 81, 82, 83, 85, 89, 92, 93, 94, 97, 98 A. B. C. D. 73 22.4 73.5 74 Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. 23. The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. Construct a boxplot for the data set. 310, 320, 450, 460, 470, 500, 520, 540,580, 600, 650, 700, 710, 840, 870, 900, 1000, 1200, 1250, 1300, 1400, 1720, 2500, 3700 Find the indicated probability. 24. A class consists of 66 women and 98 men. If a student is randomly selected, what is the probability that the student is a woman? A. B. C. D. 49/82 33/82 1/164 33/49 Find the mean of the given probability distribution 25. The number of golf balls ordered by customers of a pro shop has the following probability distribution. X 3 6 9 12 15 A. μ = 6.99 B. μ = 9 P(x) 0.14 0.05 0.36 0.35 0.10 C. μ = 7.86 D. μ = 9.66 Provide an appropriate response. Round to the nearest hundredth. 26. The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the standard deviation for the probability distribution. A. B. C. D. 1.05 0.59 0.71 0.77 Provide an appropriate response. 27. In a game, you have a 1/36 probability of winning $94 and a 35/36 probability of losing $8. What is your expected value? A. B. C. D. -$5.17 $2.61 -$7.78 $10.39 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. 28. N = 12, x = 5, p= 0.25 A. B. C. D. 0.091 0.082 0.103 0.027 Solve the problem 29. According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16. A. B. C. D. 2.8 3.5 0.2 4.0 30. The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 8. Find the standard deviation for the number of seeds germinating in each batch. A. 1.7 B. 1.3 C. 2.8 D. 16.8 31. On a multiple choice test with 19 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers. A. B. C. D. 4.8 14.3 9.5 6.3 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 . 32. A survey for brand recognition is done and it is determined that 68% of consumers have heard of 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 698 consumers who recognize the Dull Computer Company name? A. Yes B. No Find the indicated z score. The graph depicts the standard normal distribution with mean O and standard deviation 1. 33. Shaded area is 0.9599 A. B. C. D. 1.82 1.03 -1.38 1.75 If z is a standard normal variable, find the probability. 34. The probability that z lies between 0.7 and 1.98 A. B. C. D. -0.2181 0.2175 1.7341 0.2181 Solve the problem. Round to the nearest tenth unless indicated otherwise. 35. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find P45, which is the consumption level separating the bottom 45% from the top 55%. A. B. C. D. 1078.3 1021.7 1148.1 1087.8 36. Scores on a test are normally distributed with a mean of 70 and a standard deviation of 11.5. Find P31, which separates the bottom 81% from the top 19%. A. B. C. D. 0.88 0.291 80.1 73.3 Assume that X has a normal distribution, and find the indicated probability. 37. The mean is μ= 15.2 and the standard deviation is = 0.9. Find the probability that X is greater than 17. A. B. C. D. 0.9713 0.9772 0.0228 0.9821 Find the indicated probability 38. The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month? A. B. C. D. 40.82% 35.31% 90.82% 9.18% Solve the problem 39. The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 94 inches, and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49 randomly picked years will exceed 96.8 inches? A. B. C. D. 0.0808 0.0026 0.4192 0.5808 40. The weights of the fish in a certain lake are normally distributed with a mean of 19 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean weight will be between 16.6 and 22.6 lb? A. B. C. D. 0.6730 0.4032 0.0968 0.3270 Answer Key 1) C 2) C 3) A 4) A 5) The approximate amount at the center is 16 magazines. 6) B 7) A 8) A 9) A 10) D 11) A 12) C 13) B 14) C 15) C 16) D 17) B 18) C 19) D 20) B 21) C 22) D 23) C 24) B 25) D 26) D 27) A 28) C 29) B 30) B 31) A 32) A 33) D 34) D 35) B 36) C 37) C 38) D 39) A 40) A