MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - FALL 2009 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 1) For two events M and N, P(M) =.5, P(N M) =.7, and P(N M') =.2. Find P(M N). A) 0 B).22 C) 1.0 D).78 2) For two events M and N, P(M) =.8, P(N M) =.3, and P(N M') =.5. Find P(M' N). A).71 B) 1.0 C) 0 D).29 3) For mutually exclusive events X 1, X 2, and X 3, let P(X 1 ) =.56, P(X 2 ) =.15, and P(X 3 ) =.29. Also, P(Y X 1 ) =.40, P(Y X 2 ) =.30, and P(Y X 3 ) =.60. Find P(X 1 Y). A).51 B).39 C).10 D).38 4) For mutually exclusive events X 1, X 2, and X 3, let P(X 1 ) =.19, P(X 2 ) =.28, and P(X 3 ) =.53. Also, P(Y X 1 ) =.40, P(Y X 2 ) =.30, and P(Y X 3 ) =.60. Find P(X 2 Y). A).67 B).18 C).16 D).35 Solve the problem. Express the answer as a percentage. 5) At the University of Edmond, 60% of all students are classified as lower-division, and 40% are classified as upper-division. Among the lower-division students, 30% will buy a new car, and among the upper-division students, 80% will buy a new car. A student is seen buying a new car. What is the probability that (s)he is a lower-division student? A) 36% B) 64% C) 20% D) 70% 6) At the University of Edmond, 45% of all students are classified as lower-division, 35% are classified as upper-division, and 20% are graduate students. Among the lower-division students, 60% were born in Oklahoma, among the upper-division students, 40% were born in Oklahoma, and among the graduate students, 30% were born in Oklahoma. A randomly selected student was born in Oklahoma. What is the probability the (s)he is a graduate student? A) 26% B) 57% C) 13% D) 30% The table shows a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Income Level Proportion of Population Probability that Bought a New Car $0 - $29,999 40% 0.08 $30,000 - $59,999 50% 0.12 $60,,000 and over 10% 0.23 7) $30,000 - $59,999 A) 0.59 B) 0.52 C) 0.55 D) 0.53 Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. 8) Three coins are tossed, and the number of tails is noted. A) B) C) D) 0 1/8 1 3/8 2 3/8 3 1/8 0 3/16 1 5/16 2 5/16 3 3/16 0 1/3 1 1/6 2 1/6 3 1/3 0 1/6 1 1/3 2 1/3 3 1/6
9) Two balls are drawn from a bag in which there are 4 red balls and 2 blue balls. The number of blue balls is counted. A) B) C) D) 0.333 1.333 2.333 0.719 1.280 2.001 0.4 1.53 2.07 0.07 1.53 2.4 10) Four cards are drawn from a deck. The number of red tens is counted. A) B) C) 0.001 1.280 2.719 0.145 1.145 2.851 0.719 1.280 2.001 D) 0.851 1.145 2.005 Find the expected value of the random variable in the experiment. 11) Three coins are tossed, and the number of tails is noted. A) 1.75 B) 1.5 C) 1 D) 2 12) Three cards are drawn from a deck without replacement. The number of aces is counted. A).2174 B) 1 C) 1.0134 D).2308 13) 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 B) 1.33 C) 1.4 D).933 Find the expected value for the random variable. 14) x 2 3 4 5 P(x) 0.2 0.3 0.1 0.4 A) 3.4 B) 2.9 C) 3.7 D) 3.5 15) y 6 8 10 12 P(y) 0.4 0.4 0.13 0.07 A) 7.86 B) 7.74 C) 9 D) 7.34 Solve the problem. 16) 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) -$1.00 B) -$.81 C) -$.83 D) -$.85 17) Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3 for rolling a 5 or a 6, nothing otherwise. What are your expected winnings? A) -$1.00 B) $3 C) $0 D) $1.00 18) 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) 1 B).4 C).33 D).63 Evaluate the expression. 19) 7! A) 5047 B) 5033 C) 720 D) 5040
20) 5 P 4 A) 24 B) 5 C) 120 D) 1 21) 7 C 2 A) 4 B) 21 C) 120 D) 240 22) 12 C 0 A) 1 B) 12 C) 11 D) 39,916,800 23) 31 C 1 A) 30 B) 1 C) 31 D) 32 Solve the problem. 24) José has 7 shirts in his closed. He must select 5 shirts to wear at a 5-day conference. In how many different ways can he decide which shirt to wear each day, if he does not wear any shirt more than once? A) 119 B) 2520 C) 16,807 D) 120 25) 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 26) A musician plans to perform 6 selections. In how many ways can she arrange the musical selections? A) 36 B) 720 C) 6 D) 5040 27) There are 9 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? A) 84 B) 362,880 C) 504 D) 729 28) In how many ways can 4 letters be chosen from the set {A, B, C, D, E, F} if order is important and no repeats are allowed? A) 1296 B) 15 C) 24 D) 360 29) There are 11 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible? A) 55,440 B) 161,051 C) 120 D) 462 30) How many ways can an IRS auditor select 3 of 11 tax returns for an audit? A) 165 B) 6 C) 1331 D) 990 31) If the police have 7 suspects, how many different ways can they select 5 for a lineup? The order in which the suspects are lined-up is not important. A) 2520 ways B) 35 ways C) 21 ways D) 42 ways 32) Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red cards and three black cards? A) 845,000 ways B) 1,690,000 ways C) 1,267,500 ways D) 422,500 ways 33) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committee can have at most two girls? A) 4620 ways B) 5665 ways C) 5170 ways D) 4410 ways
34) A bag contains 3 blue, 4 red, and 3 green marbles. Four marbles are drawn at random from the bag. How many different samples are possible which include exactly two red marbles? A) 90 B) 18 C) 6 D) 360 A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 35) All cherry A).3636 B).1212 C).1091 D).7272 36) All lemon A) 1 B) 0 C).061 D).1212 37) 2 cherry, 1 lemon A).1818 B).7272 C).3636 D).1212 38) One of each flavor A).0667 B).2182 C).1818 D).3636 Solve the problem. 39) An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor. A).410 B).500 C).610 D).910 40) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 2 from town A, 2 from town B, and 1 from town C. A).076 B).190 C).090 D).038 Find the requested probability. 41) A family has five children. The probability of having a girl is 1. What is the probability of having exactly 2 girls and 3 2 boys? A).6252 B).3125 C).0625 D).0312 42) A family has five children. The probability of having a girl is 1. What is the probability of having no more than 3 boys? 2 A).9688 B).8125 C).5000 D).3125 A die is rolled seven times and the number of 's that come up is tallied. Find the probability of getting the given result. 43) Exactly two 's A) 0.2961 B) 0.2009 C) 0.2344 D) 0.2791 A die is rolled 19 times and the number of 's that come up is tallied. Find the probability of getting the given result. 44) More than one A) 0.1502 B) 0.8272 C) 0.1728 D) 0.8498 At the University of Edmond (EU), 33% of the students were born outside of Oklahoma. Find the probability of the event from a random sample of 10 students from EU. 45) Exactly 2 were born outside of Oklahoma. A).1990 B).1929 C).2156 D).0028
46) Exactly 4 were born in Oklahoma. A).2253 B).0547 C).2564 D).0467 47) Seven or more were born outside of Oklahoma. A).0185 B).0154 C).0028 D).0032 Find the probability of the event. 48) The probability that a radish seed will germinate is.7. The gardener plants 20 seeds and she harvests 16 radishes. A).068 B).075 C).571 D).130 49) 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).118 B).348 C).110 D).614 Find the mean for the list of numbers. Round to the nearest tenth. 50) 5, 6, 10, 5, 14, 10 A) 10.0 B) 8.8 C) 6.8 D) 8.3 Find the mean for the frequency distribution. Round to the nearest tenth. 51) Value Frequency 14 2 18 3 22 3 29 2 35 1 A) 21.9 B) 22.3 C) 26.8 D) 10.7 Find the median. 52) 25, 26, 33, 58, 62, 74, 84 A) 52 B) 33 C) 58 D) 62 53) 10, 7, 21, 11, 45, 43, 33 A) 11 B) 33 C) 21 D) 24 54) 10, 6, 22, 18, 23, 48, 40, 34 A) 22.5 B) 22 C) 23 D) 25.5 Find the mode or modes. 55) 5, 9, 20, 3, 2, 8, 42, 1, 4, 16 A) 8 B) 9 C) 10.4 D) No mode 56) 20, 31, 46, 31, 49, 31, 49 A) 31 B) 46 C) 49 D) 36.7 57) 86, 36, 32, 36, 29, 86 A) 50.8 B) 86, 36 C) 86 D) 36
58) Using the employment information in the table on Alpha Corporation, find the mean for the grouped data. Years of Service Frequency 1-7 5 8-14 3 15-21 2 A) 12.4 B) 13.1 C) 8.9 D) 9.6 Find the standard deviation. 59) 11, 7, 17, 15, 7, 18, 18, 10, 13 A) 4.1 B) 4.4 C) 4.7 D) 1.6 60) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. Find the standard deviation of the data summarized in the given frequency table. Waiting Time Number of (Minutes) Customers 0-4 25 5-9 16 10-14 14 A) 4.0899 B) 4.1276 C) 4.0620 D) 4.1138
Answer Key Testname: MATH 2053 - PRACTICE EXAM #2 1) D 2) D 3) A 4) B 5) A 6) C 7) B 8) A 9) C 10) D 11) B 12) D 13) B 14) C 15) B 16) C 17) C 18) B 19) D 20) C 21) B 22) A 23) C 24) B 25) C 26) B 27) C 28) D 29) D 30) A 31) C 32) A 33) A 34) A 35) B 36) B 37) A 38) B 39) A 40) B 41) B 42) B 43) C 44) D 45) A 46) B 47) A 48) D 49) B 50) D 51) A 52) C 53) C 54) A 55) D 56) A 57) B 58) C 59) B 60) B