MAT 205 Practice Test Chapters 12,14-18

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.1) A newly-premiered play just ended that evening at a local theater. Theater management briefly

interviews every eighth person leaving the theater to see if that person will recommend the play atthat theater to other people. Identify the type of sampling used in this example.

1)

A) Systematic samplingB) Convenience samplingC) Voluntary response samplingD) Stratified samplingE) Cluster sampling

2) An education researcher randomly selects 38 schools from one school district and interviews all theteachers at each of the 38 schools. Identify the type of sampling used in this example.

2)

A) Systematic samplingB) Cluster samplingC) Voluntary response samplingD) Attempted censusE) Stratified sampling

3) At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A schooladministrator selects a random sample of 12 of the freshmen, a random sample of 9 of thesophomores, a random sample of 11 of the juniors, and a random sample of 8 of the seniors. Shethen interviews all the students selected. Identify the type of sampling used in this example.

3)

A) Voluntary response samplingB) Cluster samplingC) Attempted censusD) Systematic samplingE) Stratified sampling

Identify the bias.4) A newspaper conducted a random telephone survey during the day regarding the percentage of

stay-at-home moms and dads in the typical household. What, if any, will be the most noticeablebias for this survey?

4)

A) Undercoverage of the populationB) Voluntary response biasC) Nonresponse biasD) Response biasE) There does not seem to be any bias.

5) A newspaper reporter randomly sampled households by telephone during various times of theday. The people sampled are within the area of the newspaper's distribution. The newspaperreporter asked, "Are you patriotic in a time of war or armed conflict?" What, if any, will be themost noticeable bias for this survey?

5)

A) Undercoverage of the populationB) Nonresponse biasC) Voluntary response biasD) Response biasE) There does not seem to be any bias.

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List the sample space and tell whether the events are equally likely.6) A family has two children; record the genders in order of birth. 6)

A) {B, G}, equally likelyB) {BB, BG, GG}, equally likelyC) {BB, BG, GB, GG}, not equally likelyD) {BB, BG, GB, GG}, equally likelyE) {BB, BG, GG}, not equally likely

7) Toss a coin five times; record the number of heads. 7)A) {0, 1, 2, 3, 4, 5}, equally likelyB) {1, 2}, equally likelyC) {0, 1, 2, 3, 4, 5}, not equally likelyD) {1, 2, 3, 4, 5}, equally likelyE) {1, 2, 3, 4, 5}, not equally likely

The plastic arrow on a spinner for a child's game stops rotating to point at a color that will determine what happens next.Determine whether the probability assignment is possible?

8) Probability of ... Red Yellow Green Blue

0.2 0.2 0.4 0.2

8)

A) Yes B) No

9) Probability of ... Red Yellow Green Blue

0.6 0.1 0.1 0.1

9)

A) Yes B) No

A professor divided the students in her business class into three groups: those who have never taken a statistics class,those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course. Find the requestedprobability.

10) If 40% of the students have never taken a statistics class, 15% have taken only one semester of astatistics class, and the rest have taken two or more semesters of statistics, what is the probabilitythat the first groupmate you meet has studied some statistics?

10)

A) 0.45 B) 0.60 C) 0.55 D) 0.15 E) 0.85

Solve the problem. Round your answer, as needed.11) In a business class, 30% of the students have never taken a statistics class, 60% have taken only one

semester of statistics, and the rest have taken two or more semesters of statistics. The professorrandomly assigns students to groups of three to work on a project for the course. What is theprobability that at least one of your two group mates has had more than one semester of statistics?

11)

A) 0.01 B) 0.19 C) 0.90 D) 0.81 E) 0.10

Find the probability or percent of the event described.12) A survey revealed that 33% of people are entertained by reading books, 47% are entertained by

watching TV, and 20% are entertained by both books and TV. What is the probability that a personwill be entertained by either books or TV?

12)

A) 0.20 B) 0.60 C) 0.6 D) 0.80 E) 1

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Solve the problem.13) At a California college, 22% of students speak Spanish, 5% speak French, and 3% speak both

languages. What is the probability that a student chosen at random from the college speaks Spanishbut not French?

13)

A) 0.17 B) 0.19 C) 0.02 D) 0.24 E) 0.2

14) Melissa is looking for the perfect man. She claims that of the men at her college, 32% are smart, 33%are funny, and 16% are both smart and funny. If Melissa is right, what is the probability that a manchosen at random from her college is neither funny nor smart?

14)

A) 0.84 B) 0.35 C) 0.51 D) 0 E) 0.67

Solve the problem. Round your answer, as needed.15) A consumer organization estimates that 34% of the households in a particular community have one

television set, 38% have two sets, and 15% have three or more sets. If two households are chosen atrandom, what is the probability that at least one has a television set?

15)

A) 0.870 B) 0.017 C) 0.757 D) 0.226 E) 0.983

Choose the best answer.16) The Multiplication Rule says that P(A and B) = P(A) × P(B). What must be true about events A and

B for this rule to apply?16)

A) The events must be independent.B) The events must be disjoint.C) The events must be independent and disjoint

17) The Addition Rule says that P(A or B) = P(A) + P(B). What must be true about events A and B forthis rule to apply?

17)

A) The events must be independent.B) Always trueC) The events must be disjoint.

Determine whether the events are disjoint, independent, neither, or both.18) In flipping a coin twice, the events of getting heads on the first flip and heads on the second flip 18)

A) Disjoint B) Independent C) Neither D) Both

19) In rolling a fair die once, the events of getting a 3 and getting a 5 19)A) Disjoint B) Independent C) Neither D) Both

Solve the problem. Round your answer, as needed.20) You roll a fair die three times. What is the probability that you roll at least one 6? 20)

A) 0.167 B) 0.579 C) 0.5 D) 0.421 E) 0.005

21) The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% TypeA, 11% Type B, and the rest Type AB. Among five donors, what is the probability that no one isType AB?

21)

A) 0.048 B) 0.200 C) 4.800 D) 0.000 E) 0.815

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22) There is a huge pile of buttons in which 29% are black, 11% are blue, 17% are orange, 24% arewhite, and the rest are clear. You close your eyes, choose a button at random, write down whatcolor it is, and then put it back in the pile. What is the probability that the third button you chooseis the first one that's clear?

22)

A) 0.125 B) 0.007 C) 0.029 D) 0.157 E) 0.531

23) A study conducted at a certain college shows that 64% of the school's graduates find a job in theirchosen field within a year after graduation. Find the probability that among 5 randomly selectedgraduates, at least one finds a job in his or her chosen field within a year of graduating.

23)

A) 0.3200 B) 0.9940 C) 0.8926 D) 0.2000

24) A manufacturing process has a 77% yield, meaning that 77% of the products are acceptable and23% are defective. If three of the products are randomly selected, find the probability that all ofthem are acceptable.

24)

A) 0.457 B) 0.231 C) 0.593 D) 0.012 E) 2.31

Use the given table to find the indicated probability.25) College students were given three choices of pizza toppings and asked to choose one favorite. The

following table shows the results.

toppings freshman sophomore junior senior

cheese 10 10 19 29

meat 29 29 10 10

veggie 10 10 29 29

Find P(favorite topping is veggie student is junior or senior).

25)

A) 0.58 B) 0.460 C) 0.500 D) 0.259 E) 0.744

Find the indicated probability.26) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd. 26)

A) 13

B) 16

C) 12

D) 23

E) 1

Find the probability or percent of the event described.27) Of the coffee makers sold in an appliance store, 6.0% have either a faulty switch or a defective cord,

2.0% have a faulty switch, and 0.8% have both defects. What percent of the coffee makers will havea defective cord?

27)

A) 4.8% B) 6.8% C) 6.0% D) 2.8% E) 4%

28) In one city, 52.2% of adults are female, 9.9% of adults are left-handed, and 5.2% are left-handedfemales. For an adult selected at random from the city, let

F = event the person is femaleL = event the person is left-handed.

Find P(F or L). Round approximations to three decimal places.

28)

A) 0.569 B) 0.621 C) 0.720 D) 0.517 E) 0.6732

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Find the indicated probability.29) At a California college, 14% of students speak Spanish, 7% speak French, and 2% speak both

languages. A student is chosen at random from the college What is the probability that the studentspeaks Spanish if she speaks French?

29)

A) 0.190 B) 0.143 C) 0.050 D) 0.020 E) 0.286

30) A box contains 12 batteries of which 5 are still working. Anne starts picking batteries one at a timefrom the box and testing them. Find the probability that she has to pick 5 batteries in order to findone that works.

30)

A) 0.044 B) 0.001 C) 6.031 D) 0.013 E) 0.017

31) A box contains 16 batteries of which 7 are still working. Anne starts picking batteries one at a timefrom the box and testing them. Find the probability that at least one of the first four works.

31)

A) 0.019 B) 0.081 C) 0.069 D) 0.900 E) 0.931

Use a tree diagram to find the indicated probability.32) In the town of Maplewood, a certain type of laptop computer is sold at just two stores. Store A has

38% of the sales, 4% of which are of defective items, and store B has 62% of the sales, 2% of whichare of defective items. A person receives one of these laptop computers as a gift. What is theprobability it is defective?

32)

A) 0.014 B) 0.04 C) 0.028 D) 0.03 E) 0.42

33) A company manufacturing electronic components for home entertainment systems buys electricalconnectors from three suppliers. It buys 27% of the connectors from supplier A, 33% from supplierB, and 40% from supplier C.It finds that 3% of the connectors from supplier A are defective, 2% of the connectors from supplierB are defective, and 4% of the connectors from supplier C are defective.If a customer buys one of these components and finds that the connector is defective, what is theprobability that it came from supplier B?

33)

A) 0.33 B) 0.264 C) 0.274 D) 0.215 E) 0.02

34) 3.9% of a population are infected with a certain disease. There is a test for the disease, however thetest is not completely accurate. 92% of those who have the disease will test positive. However 4.4%of those who do not have the disease will also test positive (false positives). What is the probabilitythat any given person will test positive? Round your answer to three decimal places if necessary.

34)

A) 0.078 B) 0.036 C) 0.042 D) 0.92 E) 0.482

35) 2.5% of a population are infected with a certain disease. There is a test for the disease, however thetest is not completely accurate. 94.9% of those who have the disease will test positive. However4.5% of those who do not have the disease will also test positive (false positives). What is theprobability that a person who tests positive actually has the disease?

35)

A) 0.351 B) 0.025 C) 0.541 D) 0.649 E) 0.949

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Create a probability model for the random variable.36) In a box of 8 batteries, 3 are dead. You choose two batteries at random from the box.

Let the random variable X be the number of good batteries you get. Find the probability model forX.

36)

A) Number good 0 1 2P(Number good) 0.107 0.536 0.357

B) Number good 0 1 2P(Number good) 0.107 0.268 0.357

C) Number good 0 1 2P(Number good) 0.141 0.469 0.391

D) Number good 0 1 2P(Number good) 0.357 0.536 0.268

E) Number good 0 1 2P(Number good) 0.055 0.436 0.509

Solve the problem.37) In a game, you have a 1/23 probability of winning $102 and a 22/23 probability of losing $9. What is

your expected value?37)

A) $4.43 B) $4.04 C) -$8.61 D) -$4.17 E) $13.04

Find the mean of the given probability distribution.38)

x P(x)0 0.141 0.062 0.423 0.144 0.24

38)

A) 2.28 B) 2.42 C) 2.32 D) 2.18

Find the standard deviation.39) In a certain town, 40% of adults have a college degree. The accompanying table describes the

probability distribution for the number of adults (among 4 randomly selected adults) who have acollege degree. Find the standard deviation for the probability distribution. x P(x)0 0.12961 0.34562 0.34563 0.15364 0.0256

39)

A) 0.98 B) 1.12 C) 0.96 D) 1.88

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Given independent random variables with means and standard deviations as shown, find the mean and standarddeviation of the specified quantity.

40) Mean SD

X 20 2Y 30 4

Find mean and standard deviation for 4Y.

40)

A) Mean = 30; SD = 16B) Mean = 120; SD = 4C) Mean = 30; SD = 4D) Mean = 30; SD = 8E) Mean = 120; SD = 16

41) Mean SD

X 40 5Y 50 4

Find mean and standard deviation for Y - 2.

41)

A) Mean = 50; SD = 2B) Mean = 50; SD = 4C) Mean = 48; SD = 4D) Mean = 48; SD = 2E) Mean = 50; SD = 6

Solve.42) Given independent random variables with means and standard deviations as shown, find the mean

and standard deviation of the variable X + 5Y . Round to two decimal places if necessary.

Mean SDX 80 6Y 50 5

42)

A) µ = 330, = 25.71B) µ = 250, = 25.71C) µ = 330, = 31D) µ = 130, = 31E) µ = 130, = 25.71

Provide an appropriate response.43) If X and Y are independent random variables then the standard deviation of the random variable

X - Y is given by which of the following expressions?43)

A) SD(X) - SD(Y)B) SD(X) + SD(Y)C) Var(X) + Var(Y)D) Var(X) + Var(Y)E) Var(X) - Var(Y)

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Solve.44) The amount of money that Maria earns in a week is a random variable with a mean of $980 and a

standard deviation of $35. The amount of money that Elena earns in a week is a random variablewith a mean of $800 and a standard deviation of $10. How much more do you expect Maria toearn in a week than Elena? What is the standard deviation of this difference? Assume that Maria'searnings are independent of Elena's earnings.

44)

A) $1780, $45B) $180, $36.40C) $180, $33.54D) $180, $25E) $1780, $36.40

Determine whether a probability model based on Bernoulli trials can be used to investigate the situation. If not, explain.45) We record the blood types (O, A, B, or AB) found in a group of 100 people. Assume that the people

are unrelated to each other.45)

A) Yes.B) No. More than two outcomes are possible.C) No.The chance of getting a particular blood group changes from one person to the next.D) No. The chance of getting a particular blood group depends on the blood groups already

recorded.E) No, 400 is more than 10% of the population.

Find the probability of the outcome described.46) Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale

testing. What is the probability that the sixth chip you test is the first bad one you find?46)

A) 0.03 B) 0.0024 C) 0.0729 D) 0.0258 E) 0.18

Determine whether a probability model based on Bernoulli trials can be used to investigate the situation. If not, explain.47) How likely is it that in a group of 300 people, the majority have blue eyes, given that 22% of the

population have blue eyes? Assume that the people are unrelated to each other.47)

A) YesB) No. More than two outcomes are possible.C) No. The chance of blue eyes changes from one person to the next.D) No. More than 10% of the population have blue eyes.E) No. 200 is more than 10% of the population.

Find the probability of the outcome described.48) Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale

testing. If you test 5 chips, what is the probability that none of the chips fail?48)

A) 0.97B) 0.8587C) 2.43 × 10-8D) 0.15E) 0.03

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49) Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presaletesting. If you test 3 chips, what is the probability that all of the chips fail?

49)

A) 2.7 × 10-5B) 0.09C) 0.9127D) 0.97E) 0.03

50) An archer is able to hit the bull's-eye 60% of the time. Assume each shot is independent of theothers. If she shoots 10 arrows, what is the probability of exactly 9 bull's-eyes?

50)

A) 0.0040 B) 0.6 C) 0.0403 D) 0.0101 E) 0.54

51) An archer is able to hit the bull's-eye 60% of the time. Assume each shot is independent of theothers. If she shoots 10 arrows, what is the probability of at least 7 bull's-eyes?

51)

A) 0.0280 B) 0.2150 C) 0.6177 D) 0.0018 E) 0.3823

52) An archer is able to hit the bull's-eye 60% of the time. Assume each shot is independent of theothers. If she shoots 10 arrows, what is the probability of at most 6 bull's-eyes?

52)

A) 0.2508 B) 0.6177 C) 0.0467 D) 0.3823 E) 0.0012

Solve the problem.53) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 5.

Find the mean for the number of seeds germinating in each batch.53)

A) 4.5 B) 7.0 C) 3.55 D) 1.5 E) 3.5

54) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 13.Find the standard deviation for the number of seeds germinating in each batch.

54)

A) 1.632 B) 0.210 C) 1.587 D) 1.568 E) 1.652

Solve.55) Suppose that 80% of tax returns are free of errors. How many returns should an IRS auditor expect

to check before finding one with errors?55)

A) 5 B) 1.25 C) 0.80 D) 80 E) 20

Solve the problem.56) On a multiple choice test with 17 questions, each question has four possible answers, one of which

is correct. For students who guess at all answers, find the standard deviation of the number ofcorrect answers.

56)

A) 1.785 B) 1.732 C) 1.749 D) 1.697 E) 1.875

57) Suppose that 12% of people are left handed. If 27 people are selected at random, what is the meanof the number of right-handers in the group?

57)

A) 23.76 B) 3.24 C) 2.85 D) 1.69 E) 13.5

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Answer the question.58) In a large statistics class, the professor has each student toss a coin 10 times and calculate the

proportion of his or her tosses that were tails. The students then report their results, and theprofessor plots a histogram of these several proportions. Should a Normal model be used here?

58)

A) A Normal model should be used because the samples are random and independent. Also, thesample size, 10, is less than 10% of the population.

B) A Normal model should not be used because the sample size, 10, is larger than 10% of thepopulation of all coins.

C) A Normal model should not be used because the population distribution is not Normal.D) A Normal model should be used because the 10 coin tosses can be thought of as a random

sample of coin tosses and are fewer than 10% of the population of all coins. Thesuccess/failure condition is also satisfied because n = 10 10.

E) A Normal model should not be used because the sample size is not large enough to satisfy thesuccess/failure condition. For this sample size, np = 5 < 10.

59) In a large statistics class, the professor has each student toss a coin 48 times and calculate theproportion of his or her tosses that were tails. The students then report their results, and theprofessor plots a histogram of these several proportions. Should a Normal model be used here?

59)

A) A Normal model should not be used because the sample size is not large enough to satisfy thesuccess/failure condition.

B) A Normal model should be used because the 48 coin tosses can be thought of as a randomsample of coin tosses and are fewer than 10% of the population of all coins. Thesuccess/failure condition is also satisfied because np = 24 10 and nq = 24 10.

C) A Normal model should be used because the samples are random and independent. Also, thesample size, 48, is less than 10% of the population. Most importantly, the original populationhas a Normal distribution.

D) A Normal model should not be used because the sample size, 48, is larger than 10% of thepopulation of all coins.

E) A Normal model should not be used because the population distribution is not Normal.

Describe the indicated sampling distribution model.60) A realtor has been told that 40% of homeowners in a city prefer to have a finished basement. She

surveys a group of 200 homeowners randomly chosen from her client list. Describe the samplingdistribution model of the proportion of homeowners in this sample who prefer a finishedbasement.

60)

A) There is not enough information to describe the distribution.B) N(40%, 3.5%)C) N(40%, 1.7%)D) N(60%, 3.5%)E) Binom(200, 40%)

In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tossesthat were heads. The students then report their results, and the professor plots a histogram of these several proportions.Use the 68-95-99.7 Rule to provide the appropriate response.

61) If the students toss the coin 80 times each, about 95% should have proportions between what twonumbers?

61)

A) 0.39 and 0.61B) 0.1118 and 0.1677C) 0.025 and 0.975D) 0.2375 and 0.7375E) 0.4875 and 0.5125

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Find the specified probability, from a table of Normal probabilities.62) Based on past experience, a bank believes that 7% of the people who receive loans will not make

payments on time. The bank has recently approved 300 loans. What is the probability that over 8%of these clients will not make timely payments?

62)

A) 0.752 B) 0.504 C) 0.248 D) 0.68 E) 0.496

63) When a truckload of oranges arrives at a packing plant, a random sample of 125 is selected andexamined. The whole truckload will be rejected if more than 8% of the sample is unsatisfactory.Suppose that in fact 9% of the oranges on the truck do not meet the desired standard. What's theprobability that the shipment will be rejected?

63)

A) 0.6966 B) 0.7803 C) 0.6517 D) 0.2197 E) 0.3483

Answer the question.64) In a large class, the professor has each person toss a coin 200 times and calculate the proportion of

his or her tosses that were tails. The students then report their results, and the professor records theproportions. One student claims to have tossed her coin 200 times and found 59% tails. What doyou think of this claim? Explain your response.

64)

A) This is a typical result. Her proportion is only 2.55 standard deviations above the mean.B) This is a fairly unusual result. Her proportion is about 2.55 standard deviations above the

mean.C) This is an extremely unlikely result. Her proportion is about 200 standard deviations above

the mean.D) This is a fairly unusual result. Her proportion is about 1.80 standard deviations above the

mean.E) This is a typical result. Her proportion is only 1.80 standard deviations above the mean.

Describe the indicated sampling distribution model.65) Statistics from a weather center indicate that a certain city receives an average of 23 inches of snow

each year, with a standard deviation of 4 inches. Assume that a Normal model applies. A studentlives in this city for 4 years. Let y represent the mean amount of snow for those 4 years. Describethe sampling distribution model of this sample mean.

65)

A) N(23, 2)B) There is not enough information to describe the distribution.C) N(23, 1)D) N(23, 4)E) Binom(23, 4)

Find the specified probability66) The number of hours per week that high school seniors spend on homework is normally

distributed, with a mean of 11 hours and a standard deviation of 3 hours. 70 students are chosen atrandom. Let y represent the mean number of hours spent on homework for this group. Find theprobability that y is between 10.2 and 11.5.

66)

A) 0.8371 B) 0.1383 C) 0.9048 D) 0.171 E) 0.0698

Find the specified probability, from a table of Normal probabilities.67) The weight of crackers in a box is stated to be 16 ounces. The amount that the packaging machine

puts in the boxes is believed to have a Normal model with mean 16.15 ounces and standarddeviation 0.3 ounces. What is the probability that the mean weight of a 50-box case of crackers isabove 16 ounces?

67)

A) 0.9994 B) 0.0002 C) 0.0004 D) 0.9998 E) 0.9996

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Answer KeyTestname: PRACTICE TEST 2 (12 4-18)

1) A2) B3) E4) C5) D6) D7) C8) A9) B

10) B11) B12) B13) B14) C15) E16) A17) C18) B19) A20) D21) E22) A23) B24) A25) B26) A27) A28) A29) E30) A31) E32) C33) D34) A35) A36) A37) D38) A39) A40) E41) C42) A43) D44) B45) B46) D47) A48) B49) A50) C51) E52) B53) E

12

Answer KeyTestname: PRACTICE TEST 2 (12 4-18)

54) E55) A56) A57) A58) E59) B60) B61) A62) C63) C64) B65) A66) C67) D

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