# Stats 100 multiple choice questions assignment 2015

1. The volume of liquid in an unopened 1- gallon can of paint is an example of _________.a) the binomial distributionb) both discrete and continuous variable c) a continuous random variabled) a discrete random variablee) a constant2. The number of defective parts in a lot of 25 parts is an example of _______.a) a discrete random variableb) a continuous random variable c) the Poisson distributiond) the normal distributione) a constantA market research team compiled the following discrete probability distribution. Inthis distribution, x represents the number of automobiles owned by a family.Answer questions 3-5 based on the above discrete probability distribution.xP(x)0 0.101 0.102 0.503 0.303. The mean (average) value of x is _____.a) 1.0 b) 1.5 c) 2.0 d) 2.5 e) 3.04. The standard deviation of x is ________.a) 0.80 b) 0.89 c) 1.00 d) 2.00 e) 2.255. Which of the following statements is true?a) This distribution is skewed to the right. b) This is a binomial distribution.c) This is a normal distribution.d) This distribution is skewed to the left. e) This distribution is bimodal.6. Twenty five items are randomly selected from a batch of 1000 items. Each of theseitems has the same probability of being defective. The probability that exactly 2 ofthe 25 are defective could best be found by _______.a) using the normal distributionb) using the binomial distributionc) using the Poisson distributiond) using the exponential distribution e) using the uniform distribution7. A fair coin is tossed 5 times. What is the probability that exactly 2 heads areobserved?a) 0.313 b) 0.073 c) 0.400 d) 0.156 e) 0.250Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularitiesin the payroll system, and orders an inspection of a random sample of vouchersissued since January 1, 2006. A sample of ten vouchers is randomly selected,without replacement, from the population of 2,000 vouchers. Each voucher in thesample is examined for errors and the number of vouchers in the sample with errorsis denoted by x.Answer questions 8-11 based on the above information.8. If 20% of the population of vouchers contain errors, P(x = 0) is _____________.a) 0.8171 b) 0.1074 c) 0.8926 d) 0.3020 e) 0.20009. If 20% of the population of vouchers contain errors, P(x > 0) is _____________.a) 0.8171 b) 0.1074 c) 0.8926 d) 0.3020 e) 1.000010. If 20% of the population of vouchers contains errors, the mean value of x is ____.a) 400 b) 2 c) 200 d) 5 e) 111. If 20% of the population of vouchers contains errors, the standard deviation of xis ______.a) 1.26 b) 1.60 c) 14.14 d) 3.16 e) 0.0012. If x is a binomial random variable with n=8 and p=0.6, what is the probabilitythat x is equal to 4?a) 0.500 b) 0.005 c) 0.124 d) 0.232 e) 0.57813. If x is a binomial random variable with n = 12 and p = 0.45, P(4 ≤ x ≤ 6) is _______?a) 0.1700 b) 0.2225 c) 0.2124 d) 0.5838 e) 0.604814. If x is n=10 anda) 0.6177 b) 0.2508 c) 0.3823 d) 0.6331 e) 0.366915. If x is n=20 anda) 0.0654 b) 0.2277 c) 0.8867 d) 0.1144 e) 0.113316. If x is n=20 anda) 0.0867 b) 0.0432 c) 0.1330 d) 0.8670 e) 0.0898a binomial random variable with p=0.6, P(x ≥ 6) is _______?a binomial random variable with p=0.3, P(x > 8) is _______?a binomial random variable with p=0.9, P(x ≤ 16) is _______?According to Cerulli Associates of Boston, 30% of all CPA financial advisors have anaverage client size between $500,000 and $1 million. Thirty-four percent have anaverage client size between $1 million and $5 million. Suppose a complete list of allCPA financial advisors is available and 18 are randomly selected from that list.Answer the questions 17-22 based on the above information.17. What is the expected number of CPA financial advisors that have an averageclient size between $500,000 and $1 million?a) 0.30 b) 0.612 c) 6.12 d) 5.40 e) 0.5418. What is the expected number with an average client size between $1 million and$5 million?a) 0.34 b) 6.12 c) 0.612 d) 5.40 e) 0.5419. What is the probability that at least eight CPA financial advisors have an averageclient size between $500,000 and $1 million?a) 0.1407 b) 0.0811 c) 0.0596 d) 0.9404 e) 0.859320. What is the probability that two, three, or four CPA financial advisors have anaverage client size between $1 million and $5 million?a) 0.0229 b) 0.0630 c) 0.1217 d) 0.7924 e) 0.207621. What is the probability that none of the CPA financial advisors have an averageclient size between $500,000 and $1 million?a) 0.0006 b) 0.9994 c) 0.0016 d) 0.0084 e) 0.012622. What is the probability that none have an average client size between $1 millionand $5 million?a) 0.0016 b) 0.9994 c) 0.0084 d) 0.0006 e) 0.012623. The number of cars arriving at a toll booth in five-minute intervals is Poissondistributed with a mean of 3 cars arriving in five-minute time intervals. Theprobability of 5 cars arriving over a five-minute interval is _______.a) 0.0940 b) 0.0417 c) 0.1500 d) 0.1008 e) 0.289024. The number of cars arriving at a toll booth in five-minute intervals is Poissondistributed with a mean of 3 cars arriving in five-minute time intervals. Theprobability of 3 cars arriving over a five-minute interval is _______.a) 0.2700 b) 0.0498 c) 0.2240 d) 0.0001 e) 0.002025. Suppose that, for every lot of 100 computer chips a company produces, anaverage of 1.4 are defective. Another company buys many lots of these chips at atime, from which one lot is selected randomly and tested for defects. If the tested lotcontains more than three defects, the buyer will reject all the lots sent in that batch.What is the probability that the buyer will accept the lots? Assume that the defectsper lot are Poisson distributed.a) 0.9463 b) 0.0537 c) 0.1128 d) 0.2417 e) 0.3452A medical researcher estimates that .00004 of the population has a rare blooddisorder. If the researcher randomly selects 100,000 people from the population,Answer questions 26-27 based on the above information using PoissonApproximation to Binomial problems.26. What is the probability that seven or more people will have the rare blooddisorder?a) 0.0298 b) 0.0511 c) 0.8894 d) 0.0595 e) 0.110627. What is the probability that more than 10 people will have the rare blooddisorder?a) 0.0081 b) 0.9972 c) 0.0019 d) 0.0028 e) 0.9919A high percentage of people who fracture or dislocate a bone see a doctor for thatcondition. Suppose the percentage is 99%. Consider a sample in which 300 peopleare randomly selected who have fractured or dislocated a bone.Answer questions 28-30 based on the above information using PoissonApproximation to Binomial problems.28. What is the expected number of people who would not see a doctor?a) 297 b) 3 c) 30 d) 300 e) 129. What is the probability that exactly five of them did not see a doctor?a) 0.0504 b) 0.9161 c) 0.1008 d) 0.1680 e) 0.899230. What is the probability that fewer than four of them did not see a doctor?a) 0.1680 b) 0.8153 c) 0.1008 d) 0.2528 e) 0.647231. Assume that a random variable has a Poisson distribution with a mean of 5occurrences per ten minutes. The number of occurrences per hour follows a Poissondistribution with λ equal to _________a) 5 b) 60 c) 30 d) 10 e) 2032. The Poisson distribution is being used to approximate a binomial distribution. Ifn=40 and p=0.06, what value of lambda would be used?a) 0.06 b) 2.4 c) 0.24 d) 24 e) 4033. The number of phone calls arriving at a switchboard in a 10 minute time periodwould best be modeled with the _________.a) binomial distributionb) hypergeometric distribution c) Poisson distributiond) hyperbinomial distribution e) exponential distribution34. The number of defects per 1,000 feet of extruded plastic pipe is best modeledwith the ________________.a) Poisson distributionb) Pascal distributionc) binomial distributiond) hypergeometric distribution e) exponential distribution35. The hypergeometric distribution must be used instead of the binomialdistribution when ______a) sampling is done with replacementb) sampling is done without replacement c) n≥5% Nd) both b and ce) there are more than two possible outcomes36. The probability of selecting 3 defective items and 7 good items from a warehousecontaining 10 defective and 50 good items would best be modeled with the _______.a) binomial distributionb) hypergeometric distribution c) Poisson distributiond) hyperbinomial distribution e) exponential distributionCircuit boards for wireless telephones are etched, in an acid bath, in batches of 100boards. A sample of seven boards is randomly selected from each lot for inspection.A batch contains two defective boards; and x is the number of defective boards in thesample.Answer questions 37-39 based on the above information.37. P(x=1) is _______.a) 0.1315 b) 0.8642 c) 0.0042 d) 0.6134 e) 0.678938. P(x=2) is _______.a) 0.1315 b) 0.8642 c) 0.0042 d) 0.6134 e) 0.003439. P(x=0) is _______.a) 0.1315 b) 0.8642 c) 0.0042 d) 0.6134 e) 0.813440. A large industrial firm allows a discount on any invoice that is paid within 30days. Of all invoices, 10% receive the discount.In a company audit, 10 invoices are sampled at random. The probability that fewerthan 3 of the 10 sampled invoices receive the discount is approximately __________.a) 0.1937 b) 0.057 c) 0.001 d) 0.3486 e) 0.929841. In a certain communications system, there is an average of 1 transmission errorper 10 seconds. Assume that the distribution of transmission errors is Poisson. Theprobability of 1 error in a period of one-half minute is approximately ________.a) 0.1493 b) 0.3333 c) 0.3678 d) 0.1336 e) 0.0342. It is known that screws produced by a certain company will be defective withprobability .01 independently of each other. The company sells the screws inpackages of 25 and offers a money-back guarantee that at most 1 of the 25 screws isdefective. Using Poisson approximation for binomial distribution, the probabilitythat the company must replace a package is approximately _________a) 0.01 b) 0.1947 c) 0.7788 d) 0.0264 e) 0.2211On Monday mornings, the First National Bank only has one teller window open fordeposits and withdrawals. Experience has shown that the average number ofarriving customers in a four-minute interval on Monday mornings is 2.8, and eachteller can serve more than that number efficiently. These random arrivals at thisbank on Monday mornings are Poisson distributed.Answer the questions 43-50 based on the above information.43. What is the probability that on a Monday morning exactly six customers willarrive in a four-minute interval?a) 0.9756 b) 0.0872 c) 0.9593 d) 0.0163 e) 0.040744. What is the probability that no one will arrive at the bank to make a deposit orwithdrawal during a four-minute interval?a) 0.9392 b) 0.1703 c) 0.0608 d) 0.0000 e) 0.829745. Suppose the teller can serve no more than four customers in any four-minuteinterval at this window on a Monday morning. What is the probability that, duringany given four-minute interval, the teller will be unable to meet the demand?a) 0.8477 b) 0.1523 c) 0.1557 d) 0.8443 e) 0.308146. Suppose the teller can serve no more than four customers in any four-minuteinterval at this window on a Monday morning. What is the probability that the tellerwill be able to meet the demand?a) 0.8477 b) 0.1557 c) 0.8443 d) 0.1523 e) 0.308147. When demand cannot be met during any given interval, a second window isopened. What percentage of the time will a second window have to be opened?a) 0.8477 b) 0.8443 c) 0.1557 d) 0.1523 e) 0.308148. What is the probability that exactly three people will arrive at the bank during atwo- minute period on Monday mornings to make a deposit or a withdrawal?a) 0.1082 b) 0.0026 c) 0.2225 d) 0.1128 e) 0.040749. What is the probability that five or more customers will arrive during an eightminute period?a) 0.1523 b) 0.0143 c) 0.6579 d) 0.3421 e) 0.847750. On Saturdays, cars arrive at Sami Schmitt’s Scrub and Shine Car Wash at the rateof 6 cars per fifteen minute interval. Using the Poisson distribution, the probabilitythat five cars will arrive during the next five minute interval is _____________.a) 0.1008 b) 0.0361 c) 0.1339 d) 0.1606 e) 0.3610Chp. 6: Questions 51-100.51. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12), thenthe height of this distribution, f(x), is …a) 1/8 b) 1/4 c) 1/12 d) 1/20 e) 1/2452. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then the mean of this distribution is _____.a) 10b) 20c) 5d) 0e) unknown53. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then the standard deviation of this distribution is __________________.a) 4.00 b) 1.33 c) 1.15 d) 2.00 e) 1.0054. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then the probability, P(9 x 11), is ____.a) 0.250 b) 0.500 c) 0.333 d) 0.750 e) 1.00055. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then the probability, P(10.0 x 11.5), is _.a) 0.250 b) 0.333 c) 0.375 d) 0.500 e) 0.75056. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then the probability, P(13 x 15), is __________________.a) 0.250 b) 0.500 c) 0.375 d) 0.000 e) 1.00057. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then P(x < 7) is __________________.a) 0.500 b) 0.000 c) 0.375 d) 0.250 e) 1.00058. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then P(x 11) is ________.a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 1.00059. If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12),then P(x 10) is __________________.a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 0.90060. If a continuous random variable x is uniformly distributed over the interval 8 to12, inclusively, then P(x = exactly 10) is __.a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 0.90061. The normal distribution is an example ofa) a discrete distributionb) a continuous distribution c) a bimodal distributiond) an exponential distribution e) a binomial distribution62. The total area underneath any normal curve is equal to _______.a) the meanb) onec) the varianced) the coefficient of variation e) the standard deviation63. The area to the left of the mean in any normal distribution is equal to _______.a) the meanb) 1c) the variance d) 0.5e) -0.564. A standard normal distribution has the following characteristics:a) the mean and the variance are both equal to 1b) the mean and the variance are both equal to 0c) the mean is equal to the varianced) the mean is equal to 0 and the variance is equal to 1e) the mean is equal to the standard deviation65. If x is a normal random variable with mean 80 and standard deviation 5, the zscore for x = 88 is ________.a) 1.8 b) -1.8 c) 1.6 d) -1.6 e) 8.066. Suppose x is a normal random variable with mean 60 and standard deviation 2.A z score was calculated for a number, and the z score is 3.4. What is x?a) 63.4b) 56.6 c) 68.6 d) 53.2 e) 66.867. Suppose x is a normal random variable with mean 60 and standard deviation 2.A z score was calculated for a number, and the z score is -1.3. What is x?a) 58.7 b) 61.3 c) 62.6 d) 57.4 e) 54.768. Let z be a normal random variable with mean 0 and standard deviation 1. Whatis P(z < 1.3)?a) 0.4032 b) 0.9032 c) 0.0968 d) 0.3485 e) 0. 548569. Let z be a normal random variable with mean 0 and standard deviation 1. Whatis P(1.3 < z < 2.3)?a) 0.4032 b) 0.9032 c) 0.4893 d) 0.0861 e) 0.008670. Let z be a normal random variable with mean 0 and standard deviation 1. Whatis P(z > 2.4)?a) 0.4918 b) 0.9918 c) 0.0082 d) 0.4793 e) 0.082071. Let z be mean 0 and P(z < -2.1)?a) 0.4821 b) -0.4821 c) 0.9821 d) 0.0179 e) -0.017972.Let z be a normal random variable withmean 0 standard deviation 1. What isP(z > -1.1)?a) 0.36432 b) 0.8643 c) 0.1357 d) -0.1357 e) -0.864373.Let z be a normal random variable withmean 0 and standard deviation 1. What is P(-2.25 < z < -1.1)?a) 0.36432 b) 0.8643 c) 0.1357 d) -0.1357 e) -0.864374. The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulbwould last longer than 1150 hours?a) 0.4987 b) 0.9987 c) 0.0013 d) 0.5013 e) 0.551375. The expected (mean) life of a particular type of light bulb is 1,000 hours with astandard deviation of 50 hours. The life ofa) 0.3643 b) 0.8643 c) 0.1235 d) 0.4878 e) 0.500076. The expected (mean) life of a particular type of light bulb is 1,000 hours with astandard deviation of 50 hours. The life of this bulb is normally distributed. What isthe probability that a randomly selected bulb would last fewer than 940 hours?a) 0.3849 b) 0.8849 c) 0.1151 d) 0.6151 e) 0.656377. Suppose you are working with a data set that is normally distributed with amean of 400 and a standard deviation of 20. Determine the value of x such that 60%of the values are greater than x.a) 404.5 b) 395.5 c) 405.0 d) 395.0 e) 415.0According to a report by Scarborough Research, the average monthly householdcellular phone bill is $60. Suppose local monthly household cell phone bills arenormally distributed with a standard deviation of $11.35.Answer questions 78-81 based on the above information.78. What is the probability that a randomly selected monthly cell phone bill is morethan $85?a) 0.4861 b) 0.9861 c) 0.6139 d) 0.5000 e) 0.013979. What is the probability that a randomly selected monthly cell phone bill isbetween $45 and $70?a) 0.8106 b) 0.9066 c) 0.7172 d) 0.4066 e) 0.310680. What is the probability that a randomly selected monthly cell phone bill isbetween $65 and $75?a) 0.2366 b) 0.1700 c) 0.4066 d) 0.0934 e) 0.670081. What is the probability that a randomly selected monthly cell phone bill is nomore than $40?a) 0.4987 b) 0.4608 c) 0.5000 d) 0.9608 e) 0.039282. According to Student Monitor, a New Jersey research firm, the average cumulatedcollege student loan debt for a graduating senior is $25,760.Assume that thestandard deviation of such student loan debt is$5,684. Thirty percent of these graduating seniors owe more than what amount?a) $28,715.68 b) $2,955.68 c) $22,804.32 d) $28,809.28 e) $28,359.6883. Let x be a binomial random variable with n=20 and p=.8. If we use the normaldistribution to approximate probabilities for this, we would use a mean of _______.a) 20 b) 16 c) 3.2 d) 8 e) 584. Let x be a binomial random variable with n=100 and p=.8. If we use the normaldistribution to approximate probabilities for this, a correction for continuity shouldbe made. To find the probability of more than 12 successes, we should find _______.a) P(x>12.5) b) P(x>12) c) P(x>11.5) d) P(x<11.5) e) P(x < 12)A study about strategies for competing in the global marketplace states that 52% ofthe respondents agreed that companies need to make direct investments in foreigncountries. It also states that about 70% of those responding agree that it is attractiveto have a joint venture to increase global competitiveness. Suppose CEOs of 95manufacturing companies are randomly contacted about global strategies.Using Normal Approximation of Binomial Distribution with correction forcontinuity, answer questions 85-88 based on above information.85. What is the probability that between 44 and 52 (inclusive) CEOs agree thatcompanies should make direct investments in foreign countries?a) 0.3869 b) 0.2389 c) 0.6258 d) 0.5013 e) 0.738986. What is the probability that more than 56 CEOs agree with that assertion?a) 0.4279 b) 0.8279 c) 0.5000 d) 0.0721 e) 0.572187. What is the probability that fewer than 60 CEOs agree that it is attractive to havea joint venture to increase global competitiveness?a) 0.5000 b) 0.0582 c) 0.4418 d) 0.9418 e) 0.558288. What is the probability that between 55 and 62 (inclusive) CEOs agree with thatassertion?a) 0.4963 b) 0.9963 c) 0.3133 d) 0.8099e) 0.183089. The average length of time between arrivals at a turnpike tollbooth is 23seconds. Assume that the time between arrivals at the tollbooth is exponentiallydistributed. What is the probability that a minute or more will elapse betweenarrivals?a) 0.9265 b) 0.0435 c) 0.4365 d) 0.0735 e) 0.500090. The average length of time between arrivals at a turnpike tollbooth is 23seconds. Assume that the time between arrivals at the tollbooth is exponentiallydistributed. If a car has just passed through the tollbooth, what is the probabilitythat no car will show up for at least 3 minutes?a) 0.0004 b) 0.9996 c) 0.4996 d) 0.0435 e) 0.9265During the summer at a small private airport in western Nebraska, the unscheduledarrival of airplanes is Poisson distributed with an average arrival rate of 1.12 planesper hour.Answer questions 91-93 based on the above information.91. What is the average interarrival time between planes (in minutes)?a) 53.6 b) 67.2 c) 53.4 d) 60e) 58.8892. What is the probability that at least 2 hours will elapse between plane arrivals?a) 0.5000 b) 0.8935 c) 0.3935 d) 0.6065 e) 0.106593. What is the probability of two planes arriving less than 10 minutes apart?a) 0.8297 b) 0.1703 c) 0.6703 d) 0.3297 e) 0.500094. The probability that a call to an emergency help line is answered in less than 10seconds is 0.8. Assume that the calls are independent of each other. Using the normalapproximation for binomial with a correction for continuity, the probability that atleast 75 of 100 calls are answered within 10 seconds is approximately _______a) 0.8b) 0.1313 c) 0.5235 d) 0.9154 e) 0.868795. Inquiries arrive at a record message device according to a Poisson process of rate15 inquiries per minute. The probability that it takes more than 12 seconds for thefirst inquiry to arrive is approximately _________a) 0.05b) 0.75c) 0.25d) 0.27e) 0.7396. On Saturdays, cars arrive at Sam Schmitt’s Scrub and Shine Car Wash at the rateof 6 cars per fifteen minute interval. The probability that at least 2 minutes willelapse between car arrivals is _____________.a) 0.0000 b) 0.4493 c) 0.1353 d) 1.0000 e) 1.022597. On Saturdays, cars arrive at Sam Schmitt’s Scrub and Shine Car Wash at the rateof 6 cars per fifteen minute interval. The probability that less than 10 minutes willelapse between car arrivals is _________.a) 0.8465 b) 0.9817 c) 0.0183 d) 0.1535 e) 0.212598. Incoming phone calls generally are thought to be Poisson distributed. If anoperator averages 2.2 phone calls every 30 seconds, what is the expected (average)amount of time between calls (in seconds)?a) 66b) 30c) 13.64 d) 60e) 27.2799. Incoming phone calls generally are thought to be Poisson distributed. If anoperator averages 2.2 phone calls every 30 seconds, what is the probability that aminute or more would elapse between incoming calls?a) 0.9877 b) 0.5123c) 0.4877 d) 0.5000 e) 0.0123100. Incoming phone calls generally are thought to be Poisson distributed. If anoperator averages 2.2 phone calls every 30 seconds, what is the probability that atleast two minutes would elapse between incoming calls?a) 0.0002 b) 0.9998 c) 0.4998 d) 0.5000 e) 0.5002

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