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 and 3 2 boys? A).6252 B).3125 C).0312 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).0313 C).3125 D).1875 A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. 3) Exactly three fours A).032 B).003 C).161 D).402 A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. 4) More than three twos A).433 B).403 C).564 D).905 At the University of Edmond, 33% of all students have majors from the College of Business. Find the probability of the event from a random sample of 10 students randomly selected from the University. 5) Exactly 4 have majors from colleges other than the College of Business. A).0547 B).2253 C).2564 D) ) Two or fewer have majors from the College of Business. A).1080 B).1990 C).3070 D).2888 Find the probability of the event. 7) A 10-question multiple choice test has 4 possible answers for each question. A student guesses at least 6 correct answers. [Assume the student didn't study, and the probability of a correct answer is only 1/4.] A).989 B).020 C).118 D).995 8) The probability that a radish seed will germinate is.7. The gardener plants 20 seeds and she harvests 16 radishes. A).075 B).068 C).130 D).571 9) 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).614 C).348 D).110 Decide whether or not the matrix is a probability vector. 10) )

2 12) Decide whether or not the matrix is a transition matrix. 13) ) Decide whether or not the transition matrix is regular. 15) A) No B) Yes 16) A) No B) Yes 17) For the transition matrix, find the probability that state 2 changes to state 1 after 2 repetitions of the experiment. 18) A) 0.42 B) 0.49 C) 0.36 D) 0.18 Construct the transition diagram and the transition matrix that represents the data. 19) If it snows today, there is a(n) 80 percent chance of snow tomorrow; however if it does not snow today, there is a(n) 40 percent chance that it will not snow tomorrow. A) B) C) D)

3 20) 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) L C I L C I Find the requested long-range probabilities based on the transition matrix or data given. B) L C I L C I ) 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) Find the mean for the list of numbers. Round to the nearest tenth. 22) 16, 9, 24, 16 A) 24.7 B) 16.3 C) 16.8 D) ) 6, 6, 9, 6, 11, 10 A) 8.5 B) 9.6 C) 6.5 D) 8.0 Find the mean for the frequency distribution. Round to the nearest tenth. 24) Value Frequency A) 25.1 B) 7.2 C) 23.3 D) ) Value Frequency A) B) C) D) 82.1

4 Find the median. 26) 3, 6, 12, 23, 44, 44, 50 A) 23 B) 26 C) 44 D) 12 27) 3, 2, 22, 16, 50, 38, 31 A) 23 B) 16 C) 22 D) 31 28) 10, 1, 21, 12, 23, 44, 37, 37 A) 23 B) 21 C) 22 D) 23.5 Find the mode or modes. 29) 5, 9, 97, 3, 2, 8, 77, 1, 4, 16 A) No mode B) 21.6 C) 8 D) 9 30) 20, 34, 46, 34, 49, 34, 49 A) 34 B) 38 C) 46 D) 49 31) 98, 39, 32, 39, 29, 98 A) 39 B) 55.8 C) 98, 39 D) 98 Find the mean. 32) The six Cane brothers spent $61.48, $76.06, $48.04, $45.78, $62.94, and $58.08 on groceries. Find the mean grocery bill. A) $70.48 B) $88.10 C) $58.48 D) $58.73 Solve the problem. 33) 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) Find the standard deviation. 34) 7, 15, 20, 19, 18, 20, 17, 11, 6 A) 5.2 B) 1.8 C) 5.5 D) ) 5, 4, 7, 6, 19, 6, 8, 8, 6 A) 4.2 B) 4.8 C) 4.4 D) 1.0

5 Find the standard deviation of the data summarized in the given frequency table. 36) 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. Round your answer to one decimal place. Waiting time (minutes) Number of customer A) 5.5 B) 5.3 C) 5.4 D) 5.0 Note: P.L. Chebyshev ( , Russian) wrote a theorem that states for any distribution of numerical data, at least 1-1 k2 of the numbers lie within k standard deviations of the mean. Remark: The statement of this theorem will not be provided on the actual test. In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev's theorem to tell the probability that a number lies in the following interval. Round your results to the nearest whole percent. 37) Between 26 and 74 A) At least 90% B) At least 93% C) At least 96% D) At least 94% 38) Less than 20 or more than 80 A) At most 6% B) At most 4% C) At most 1% D) At most 2% Find the standard deviation for the given data. 39) The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below. Round results to four decimal places A) B) C) D) Solve the problem. 40) Find the percent of the area under the standard normal curve between z = 1.41 and z = A) 7.9% B) 7.8% C) 7.7% D) 7.85% 41) Find the percent of the area under the standard normal curve between z = and z = A) 43.1% B) 43.9% C) 43.4% D) 43.5% 42) Find the percent of the area under the standard normal curve between z = and z = A) 87.7% B) 11.3% C) 11.1% D) 86.8% Find a z-score satisfying the given condition. 43) 4% of the total area is to the right of z. A) B) 1.74 C) 1.76 D) 1.75

6 44) 74.9% of the total area is to the left of z. A) 0.68 B) C) 0.66 D) 0.67 Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. 45) 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) 1% B) 2% C) 98% D) 3% 46) The average size of the fish in a lake is 11.4 inches, with a standard deviation of 3.2 inches. Find the probability of catching a fish longer than 17 inches. A) 5% B) 96% C) 4% D) 8% 47) 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) 90% B) 8% C) 19% D) 9% 48) 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) 60% D) 40% A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the approximate number of bulbs that can be expected to last the specified period of time. 49) At least 500 hours A) 5000 B) 1000 C) 2500 D) ) Between 500 hours and 675 hours A) 2256 B) 4800 C) 4700 D) ) Between 290 hours and 540 hours A) 3190 B) 1639 C) 1641 D) 3185 Solve the problem. 52) If the life, in years, of a washing machine is normally distributed with a mean of 16 years and a standard deviation of 2.9 years, what should be the guarantee period if the company wants less than 1% of the machines to fail while under warranty? A) Less than years B) More than years C) Less than years D) More than years 53) If the life of a car engine, calculated in miles, is normally distributed, with a mean of 180,000 miles and a standard deviation of 11,500 miles, what should be the guarantee period if the company wants less than 2% of the engines to fail while under warranty? A) Less than 203,690 miles B) Less than 170,340 miles C) Less than 146,880 miles D) Less than 156,310 miles Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of the indicated results. 54) Exactly 250 heads A).031 B).040 C).016 D).032

7 55) Exactly 275 heads A).003 B).320 C).030 D) ) 240 heads or more A).816 B).874 C).829 D) ) 230 heads or less A).037 B).959 C).041 D).042 Find the probability of the result using the normal curve approximation to the binomial distribution. 58) A die is rolled 72 times and ten threes come up. A).060 B).099 C).104 D).544 Solve the problem using the normal curve approximation to the binomial distribution. 59) In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions. A).8962 B).1038 C).0420 D) ) 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).0869 B).0823 C).0934 D).9066

8 Answer Key Testname: MATH PRACTICE EXAM #2 1) B 2) D 3) A 4) A 5) A 6) C 7) B 8) C 9) C 10) B 11) A 12) B 13) A 14) B 15) B 16) A 17) A 18) A 19) B 20) A 21) A 22) B 23) D 24) A 25) C 26) A 27) C 28) C 29) A 30) A 31) C 32) D 33) C 34) C 35) C 36) B 37) D 38) B 39) A 40) C 41) D 42) A 43) D 44) D 45) B 46) C 47) D 48) D 49) C 50) D 51) D 52) C 53) D 54) D 55) A 56) D 57) C 58) C 59) B 60) C

Math 227 (Statistics) Chapter 6 Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Math 227 (Statistics) Chapter 6 Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Using the following uniform density curve, answer the