MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - SUMMER DR. DAVID BRIDGE

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1 MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - SUMMER 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) ) 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) ) 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) ) 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

2 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) Page Ref: 512 B) C) D) ) Three balls are drawn from a bag containing 5 red and 3 green balls. The number of green balls is counted. A) Page Ref: 512 B) 0 1/6 1 1/3 2 1/3 3 1/6 C) 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: ) Three cards are drawn from a deck without replacement. The number of aces is counted. A).2174 B).2308 C) 1 D) Page Ref: ) 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

3 Find the expected value for the random variable. 15) x P(x) A) B) 3.2 C) 3.5 D) 4.2 Page Ref: ) z P(z) A) 7.8 B) 9 C) 5.13 D) 9.72 Page Ref: ) A business bureau gets complaints as shown in the following table. Find the expected number of complaints per day. Complaints per Day Probability A) 2.98 B) 3.01 C) 2.73 D) 2.85 Page Ref: 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: ) 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: ) 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: ) 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: ) 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:

4 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: Decide whether or not the matrix is a probability vector. 24) A) Yes B) No Page Ref: ) A) Yes B) No Page Ref: ) A) Yes B) No Page Ref: ) A) Yes B) No Page Ref: Decide whether or not the matrix is a transition matrix. 28) A) Yes B) No Page Ref: ) A) No B) Yes Page Ref: ) A) Yes B) No Page Ref:

5 31) A) No B) Yes Page Ref: Find the equilibrium vector for the transition matrix. 32) A) [ ] B) [ ] C) [ ] D) [ ] Page Ref: ) A) [ ] B) [ ] C) [ ] D) [ ] Page Ref: ) A) [ ] B) [ ] C) [0 1] D) [ ] Page Ref: 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) Page Ref: B) C) D) None of these.

6 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: L C I L C I L C I 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 A) B) C) D) Page Ref: ) 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) [ ] B) [ ] C) [ ] D) [ ] Page Ref: 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: ) 5, 4, 10, 4, 13, 9 A) 9.0 B) 6.0 C) 7.5 D) 8.0 Page Ref: 550

7 Find the mean for the frequency distribution. Round to the nearest tenth. 41) Value Frequency A) 25.3 B) 26.5 C) 6.3 D) 23.7 Page Ref: ) Value Frequency A) B) C) 85.6 D) Page Ref: Find the median. 43) 4, 5, 10, 27, 38, 44, 46 A) 10 B) 27 C) 25 D) 38 Page Ref: ) 9, 3, 24, 20, 50, 41, 37 A) 24 B) 37 C) 26 D) 20 Page Ref: ) 6, 13, 26, 28, 32, 38 A) 27 B) 23.5 C) 28 D) 26 Page Ref: ) 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

8 48) 20, 26, 46, 26, 49, 26, 49 A) 49 B) 34.6 C) 26 D) 46 Page Ref: ) 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 $ for last week. Find the mean wage. A) $ B) $ C) $ D) $ Page Ref: 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 A) B) C) D) Page Ref: 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: ) 141, 296, 284, 295, 264, 105, 182, 165, 248 A) 27.5 B) 77.6 C) 72.6 D) 68.4 Page Ref: 564

9 Find the standard deviation of the data summarized in the given frequency table. 54) Find the standard deviation. Data Frequency A) B) C) D) Page Ref: ) The test scores of 40 students are summarized in the frequency table below. Find the standard deviation. Score Students 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: Round results to one decimal place. A) 10,368.0 B) 18.9 C) 34.0 D) Page Ref: 564 Solve the problem. 57) Find the percent of the area under the standard normal curve between z = 1.41 and z = A) 7.8% B) 7.7% C) 7.9% D) 7.85% Page Ref: ) Find the percent of the area under the standard normal curve between z = and z = A) 43.5% B) 43.1% C) 43.4% D) 43.9% Page Ref: ) Find the percent of the area under the standard normal curve between z = and z = A) 90.4% B) 90.8% C) 95.3% D).93% Page Ref:

10 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: ) 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: ) 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: ) 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: ) 265 heads or more A).089 B).093 C).910 D).097 Page Ref: ) 240 heads or more A).816 B).874 C).829 D).826 Page Ref: ) 230 heads or less A).037 B).959 C).041 D).042 Page Ref:

11 69) 251 heads or less A).552 B).548 C).448 D).536 Page Ref: 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: x4-1 71) lim x 1 x - 1 A) 4 B) 2 C) 0 D) Does not exist Page Ref: ) lim x 49 x - 49 x - 49 A) B) 0 C) D) Does not exist Page Ref: e 2x ) lim x 0 x A) B) C) 5 D) Does not exist Page Ref: 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: ) lim x -3 x2-2x - 15 x + 3 A) -8 B) 5 C) 0 D) Does not exist Page Ref:

12 Answer Key Testname: MATH 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

13 Answer Key Testname: MATH 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