MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - SUMMER 2006 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested probability. 1) A family has five children. The probability of having a girl is 1. What is the probability of having exactly 2 girls 2 and 3 boys? A).6252 B).0625 C).3125 D).0312 2) A family has five children. The probability of having a girl is 1. What is the probability of having at least 4 girls? 2 A).1563 B).1875 C).0313 D).3125 At the University of Edmond, with an extremely large population, 33% of all students belong to a student organization. Find the probability of the event from a random sample of 10 students. 3) Exactly 4 do not belong to a student organization. A).0467 B).2253 C).0547 D).2564 4) Two or less belong to a student organization. A).1990 B).3070 C).1080 D).2888 Find the requested probability. 5) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives? A).0080 B).5360 C).3125 D).9688 6) A child rolls a 6-sided die 6 times. What is the probability of the child rolling no more than three twos? A).9913 B).3812 C).9649 D).6774 Find the probability of the event. 7) The probability that a radish seed will germinate is 0.7. The gardener plants 20 seeds and she harvests 16 radishes. A).571 B).068 C).075 D).130 8) A battery company has found that the defective rate of its batteries is.03. Each day, 22 batteries are randomly tested. On Tuesday, 1 is found to be defective. A).614 B).118 C).110 D).348
Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. 9) Three coins are tossed, and the number of tails is noted. A) 0 3/16 1 5/16 2 5/16 3 3/16 Page Ref: 512 B) 0 1/8 1 3/8 2 3/8 3 1/8 C) 0 1/6 1 1/3 2 1/3 3 1/6 D) 0 1/3 1 1/6 2 1/6 3 1/3 10) Four cards are drawn from a deck. The number of red tens is counted. A) 0.145 1.145 2.851 Page Ref: 512 B) 0.719 1.280 2.001 C) 0.001 1.280 2.719 D) 0.851 1.145 2.005 11) Three balls are drawn from a bag containing 5 red and 3 green balls. The number of green balls is counted. A) 0.018 1.268 2.536 3.179 Page Ref: 512 B) 0 1/6 1 1/3 2 1/3 3 1/6 C) 0.179 1.536 2.268 3.018 D) 0 1/3 1 1/6 2 1/6 3 1/3 Find the expected value of the random variable in the experiment. 12) Three coins are tossed, and the number of tails is noted. A) 1 B) 1.75 C) 2 D) 1.5 Page Ref: 514 13) Three cards are drawn from a deck without replacement. The number of aces is counted. A).2174 B).2308 C) 1 D) 1.0134 Page Ref: 514 14) A bag contains six marbles, of which four are red and two are blue. Suppose two marbles are chosen at random and X represents the number of red marbles in the sample. A) 1.33 B) 1 C) 1.4 D).933 Page Ref: 514
Find the expected value for the random variable. 15) x 2 3 4 5 P(x) 0.1 0.1 0.3 0.5 A) 4.00000006 B) 3.2 C) 3.5 D) 4.2 Page Ref: 514-515 16) z 3 6 9 12 15 P(z) 0.14 0.36 0.36 0.04 0.10 A) 7.8 B) 9 C) 5.13 D) 9.72 Page Ref: 514-515 17) A business bureau gets complaints as shown in the following table. Find the expected number of complaints per day. Complaints per Day 0 1 2 3 4 5 Probability.04.11.26.33.19.07 A) 2.98 B) 3.01 C) 2.73 D) 2.85 Page Ref: 514-515 Solve the problem. 18) Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3000 tickets are sold at $1.00 each, find the expected value of winning for a person who buys 1 ticket. A) -$.81 B) -$.85 C) -$1.00 D) -$.83 Page Ref: 514-515 19) If 5 apples in a barrel of 25 apples are rotten, what is the expected number of rotten apples in a sample of 2 apples? A).4 B).33 C) 1 D).63 Page Ref: 514-517 20) From a group of 3 men and 4 women, a delegation of 2 is selected. What is the expected number of men in the delegation? A).86 B).48 C) 1 D).57 Page Ref: 514-517 21) If 3 balls are drawn from a bag containing 3 red and 4 blue balls, what is the expected number of red balls in the sample? A) 1.39 B) 1.29 C).89 D) 1.54 Page Ref: 514-517 22) A contractor is considering a sale that promises a profit of $25,000 with a probability of.7 or a loss (due to bad weather, strikes, and such) of $11,000 with a probability of.3. What is the expected profit? A) $25,200 B) $14,200 C) $14,000 D) $17,500 Page Ref: 514-517
23) If 2 cards are drawn from a deck of 52 cards, what is the expected number of spades? A).75 B).50 C).25 D).47 Page Ref: 517-518 Decide whether or not the matrix is a probability vector. 24) 0.59999998 0.9 0.8 A) Yes B) No Page Ref: 524-525 25) 4 5 1 5 A) Yes B) No Page Ref: 524-525 26) 0 0.1 0.4 0.5 A) Yes B) No Page Ref: 524-525 27) 0.6 0.8-0.4 A) Yes B) No Page Ref: 524-525 Decide whether or not the matrix is a transition matrix. 28) -0.9 1.1 0.1 0.1 A) Yes B) No Page Ref: 522-523 29) 8 10 2 10 2 10 8 10 A) No B) Yes Page Ref: 522-523 30).1.9.3.7 A) Yes B) No Page Ref: 522-523
31).7.2.1.2.4.5.4.4.2 A) No B) Yes Page Ref: 522-523 Find the equilibrium vector for the transition matrix. 32) 0.2 0.8 0.5 0.5 A) [0.385 0.615] B) [0.286 0.714] C) [0.615 0.385] D) [0.714 0.286] Page Ref: 527-529 33) 2 3 1 4 1 3 3 4 A) [0.571 0.429] B) [0.471 0.529] C) [0.529 0.471] D) [0.429 0.571] Page Ref: 527-529 34) 3 4 1 4 0 1 A) [ - 1 4 5 4 ] B) [ 1 4 3 4 ] C) [0 1] D) [ 3 4 1 4 ] Page Ref: 527-529 Construct the transition matrix that represents the data. 35) If it snows today, there is a 60 percent chance of snow tomorrow; however if it does not snow today, there is a 70 percent chance that it will not snow tomorrow. Assume that "snow" is state 1 and "not snow" is state 2. A) 0.6 0.4 0.7 0.3 Page Ref: 522-523 B) 0.6 0.4 0.3 0.7 C) 0.6 0.7 0.4 0.3 D) None of these.
36) Fifty percent of those who call themselves liberal for the last election will vote as liberals in the next election, 15% will vote as conservatives, and 35% will vote as independents. 70% of those who voted as conservatives in the last election will do so in the next election, while 9% will vote as liberals, and 21% will vote as independents. 88% of those who voted as independents in the last election will do so in the next election, 10% will vote as liberals, and 2% will vote as conservatives. A) B) C) L C I L C I L C I Page Ref: 522-523 L C I 0.35 0.15 0.5 0.21 0.7 0.09 0.88 0.02 0.1 L C I 0.5 0.15 0.35 0.7 0.09 0.21 0.88 0.1 0.02 L C I 0.5 0.15 0.35 0.09 0.7 0.21 0.1 0.02 0.88 Find the requested long-range probabilities based on the transition matrix or data given. 37) The probability that an assembly line works correctly depends on whether the line worked correctly the last time. Find the long-range probability that the line will work correctly. works doesn't works doesn't 0.6 0.4 0.5 0.5 A) 0.570 B) 0.600 C) 0.556 D) 0.444 Page Ref: 527-528 38) In one town there are only two cello teachers. In a given semester, the probability that a student will switch from Carol Mosely to Betty Roberts is 0.5 The probability that a student of Betty Roberts will switch to Carol Mosely is 0.1. Find the long-range prediction for the proportion of students with each teacher. A) [0.167 0.833] B) [0.475 0.525] C) [0.500 0.500] D) [0.833 0.167] Page Ref: 527-528 Find the mean for the list of numbers. Round to the nearest tenth. 39) 16, 7, 23, 16 A) 23 B) 14 C) 16 D) 15.5 Page Ref: 550 40) 5, 4, 10, 4, 13, 9 A) 9.0 B) 6.0 C) 7.5 D) 8.0 Page Ref: 550
Find the mean for the frequency distribution. Round to the nearest tenth. 41) Value Frequency 14 3 20 4 25 5 28 5 32 2 A) 25.3 B) 26.5 C) 6.3 D) 23.7 Page Ref: 551-552 42) Value Frequency 150 2 171 3 259 4 312 7 354 1 380 2 A) 270.9 B) 302.8 C) 85.6 D) 259.3 Page Ref: 551-552 Find the median. 43) 4, 5, 10, 27, 38, 44, 46 A) 10 B) 27 C) 25 D) 38 Page Ref: 554 44) 9, 3, 24, 20, 50, 41, 37 A) 24 B) 37 C) 26 D) 20 Page Ref: 554 45) 6, 13, 26, 28, 32, 38 A) 27 B) 23.5 C) 28 D) 26 Page Ref: 554 46) 9, 2, 29, 11, 21, 47, 40, 37 A) 25 B) 21 C) 29 D) 24.5 Page Ref: 554 Find the mode or modes. 47) 5, 9, 62, 3, 2, 8, 43, 1, 4, 16 A) 8 B) 9 C) 14.7 D) No mode Page Ref: 555
48) 20, 26, 46, 26, 49, 26, 49 A) 49 B) 34.6 C) 26 D) 46 Page Ref: 555 49) 96, 48, 32, 48, 29, 96 A) 96 B) 48 C) 58.2 D) 96, 48 Page Ref: 555 Find the mean. 50) Frank's Furniture employees earned $444.33, $542.03, $354.43, $504.45, $457.15, and $544.38 for last week. Find the mean wage. A) $557.35 B) $474.46 C) $711.69 D) $569.35 Page Ref: 550-552 Solve the problem. 51) Using the employment information in the table on Alpha Corporation, find the mean for the grouped data. Years of Service Frequency 1-5 5 6-10 20 11-15 25 16-20 10 21-25 5 26-30 3 A) 13.57 B) 12.93 C) 10.83 D) 15.50 Page Ref: 551-553 Find the standard deviation. 52) 8, 16, 14, 6, 17, 5, 18, 7, 17 A) 5.4 B) 5.1 C) 5.8 D) 1.5 Page Ref: 564 53) 141, 296, 284, 295, 264, 105, 182, 165, 248 A) 27.5 B) 77.6 C) 72.6 D) 68.4 Page Ref: 564
Find the standard deviation of the data summarized in the given frequency table. 54) Find the standard deviation. Data Frequency 10 4 12 5 14 8 19 2 20 6 A) 4.3589 B) 3.7305 C) 3.2904 D) 1.7819 Page Ref: 566 55) The test scores of 40 students are summarized in the frequency table below. Find the standard deviation. Score Students 50-59 8 60-69 9 70-79 7 80-89 8 90-99 8 A) 14.4 B) 13 C) 15.1 D) 13.7 Page Ref: 566 Find the standard deviation for the given data. 56) Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores: 40 17 34.0 20 15 47 67 Round results to one decimal place. A) 10,368.0 B) 18.9 C) 34.0 D) 8228.6 Page Ref: 564 Solve the problem. 57) Find the percent of the area under the standard normal curve between z = 1.41 and z = 2.83. A) 7.8% B) 7.7% C) 7.9% D) 7.85% Page Ref: 574-576 58) Find the percent of the area under the standard normal curve between z = -2.36 and z = -0.14. A) 43.5% B) 43.1% C) 43.4% D) 43.9% Page Ref: 574-576 59) Find the percent of the area under the standard normal curve between z = -1.68 and z = 1.68. A) 90.4% B) 90.8% C) 95.3% D).93% Page Ref: 574-576
Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. 60) A machine produces bolts with an average diameter of.30 inches and a standard deviation of.01 inches. What is the probability that a bolt will have a diameter greater than.32 inches? A) 3% B) 1% C) 98% D) 2% Page Ref: 577 61) The mean monthly income of trainees at a local mill is $1100 with a standard deviation of $150. Find the probability that a trainee earns less than $900 a month. A) 19% B) 90% C) 9% D) 8% Page Ref: 577 62) A machine fills quart soda bottles with an average of 32.3 oz per bottle, with a standard deviation of 1.2 oz. What is the probability that a filled bottle will contain less than 32 oz? A) 38% B) 41% C) 40% D) 60% Page Ref: 577 At one high school, students can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are: 63) Greater than 15.2 seconds A) 48% B) 50% C) 68% D) 34% Page Ref: 578 64) Less than 17 seconds A) 98% B) 84% C) 2.5% D) 97.7% Page Ref: 578 Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of the indicated results. 65) Exactly 250 heads A).040 B).016 C).031 D).032 Page Ref: 587-588 66) 265 heads or more A).089 B).093 C).910 D).097 Page Ref: 587-588 67) 240 heads or more A).816 B).874 C).829 D).826 Page Ref: 587-588 68) 230 heads or less A).037 B).959 C).041 D).042 Page Ref: 587-588
69) 251 heads or less A).552 B).548 C).448 D).536 Page Ref: 587-588 Use a calculator to estimate the limit. 70) lim x 4 x2-7x + 12 x2-5x + 4 A) 9 B) -9 C) 5 D) Does not exist Page Ref: 598-599 x4-1 71) lim x 1 x - 1 A) 4 B) 2 C) 0 D) Does not exist Page Ref: 598-599 72) lim x 49 x - 49 x - 49 A) 0.1890 B) 0 C) 0.0714 D) Does not exist Page Ref: 598-599 e 2x - 1 73) lim x 0 x A) 0.0067 B) 1.6094 C) 5 D) Does not exist Page Ref: 598-599 Use the properties of limits to evaluate the limit if it exists. 74) lim x 0 x3 + 12x2-5x 5x A) 0 B) -1 C) 5 D) Does not exist Page Ref: 601-604 75) lim x -3 x2-2x - 15 x + 3 A) -8 B) 5 C) 0 D) Does not exist Page Ref: 601-604
Answer Key Testname: MATH 2053 - PRACTICE EXAM #2 1) C 2) B 3) C 4) B 5) A 6) A 7) D 8) D 9) B 10) D 11) C 12) D 13) B 14) A 15) D 16) A 17) C 18) D 19) A 20) A 21) B 22) B 23) B 24) B 25) A 26) A 27) B 28) B 29) B 30) A 31) A 32) A 33) D 34) C 35) B 36) C 37) C 38) A 39) D 40) C 41) D 42) A 43) B 44) A 45) A 46) A 47) D 48) C 49) D 50) B 51) B 52) A 53) C
Answer Key Testname: MATH 2053 - PRACTICE EXAM #2 54) B 55) A 56) B 57) B 58) A 59) B 60) D 61) C 62) C 63) B 64) D 65) D 66) D 67) D 68) C 69) A 70) A 71) A 72) C 73) C 74) B 75) A