Ch. 4, 5, 6 Name___________________________________ 03/24/2010 Math 227 Exam #2

Ch. 4, 5, 6 Name___________________________________03/24/2010 Math 227 Exam #2_____________________________________________________________________________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Makesure that you input all you answers on the correct ScanTron.

Express the indicated degree of likelihood as a probability value.1) "You have a 50-50 chance of choosing the correct answer." 1)

A) 50 B) 0.9 C) 0.25 D) 0.50

2) "There is a 40% chance of rain tomorrow." 2)A) 40 B) 4 C) 0.40 D) 0.60

3) "You cannot determine the exact decimal-number value of ." 3)A) 1 B) 0.5 C) 0 D) 3.14

4) "It will definitely turn dark tonight." 4)A) 0.67 B) 1 C) 0.30 D) 0.5

5) "You have one chance in ten of winning the race." 5)A) 0.5 B) 0.10 C) 1 D) 0.90

Answer the question.6) Which of the following cannot be a probability? 6)

A) 23 B) 3

5 C) 53 D) 1

2

7) What is the probability of an impossible event? 7)A) -1 B) 0.1 C) 1 D) 0

8) On a multiple choice test with four possible answers for each question, what is the probability ofanswering a question correctly if you make a random guess?

8)

A) 12 B) 1

4 C) 34 D) 1

Find the indicated probability.9) A sample space consists of 14 separate events that are equally likely. What is the probability of

each?9)

A) 1 B) 0 C) 114 D) 14

10) On a multiple choice test, each question has 7 possible answers. If you make a random guess onthe first question, what is the probability that you are correct?

10)

A) 7 B) 17 C) 0 D) 1

11) A die with 8 sides is rolled. What is the probability of rolling a number less than 7? 11)

A) 18 B) 7

8 C) 6 D) 34

1

12) A bag contains 2 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomlyselected from the bag, what is the probability that it is blue?

12)

A) 15 B) 3

10 C) 13 D) 1

7

13) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dicewill be 4?

13)

A) 3 B) 23 C) 11

12 D) 112

14) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leapyears.

14)

A) 31365 B) 1

12 C) 1365 D) 1

31

15) In a poll, respondents were asked whether they had ever been in a car accident. 127 respondentsindicated that they had been in a car accident and 299 respondents said that they had not been in acar accident. If one of these respondents is randomly selected, what is the probability of gettingsomeone who has been in a car accident? Round to the nearest thousandth, if necessary.

15)

A) 0.425 B) 0.702 C) 0.008 D) 0.298

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.16) Is it "unusual" to get a 12 when a pair of dice is rolled? 16)

A) No B) Yes

17) Is it "unusual" to get 6 when a pair of dice is rolled? 17)A) No B) Yes

18) Assume that a study of 300 randomly selected school bus routes showed that 280 arrived on time.Is it "unusual" for a school bus to arrive late?

18)

A) Yes B) No

19) Assume that a study of 500 randomly selected school bus routes showed that 478 arrived on time.Is it "unusual" for a school bus to arrive late?

19)

A) Yes B) No

20) If you are told that a mystery person's name begins with a consonant, would it be "unusual" toguess the first letter of that person's name?

20)

A) No B) Yes

21) If you drew one card from a standard deck, would it be "unusual" to draw a 5? 21)A) Yes B) No

22) Assume that one student in your class of 27 students is randomly selected to win a prize. Would itbe "unusual" for you to win?

22)

A) No B) Yes

2

Estimate the probability of the event.23) The data set represents the income levels of the members of a country club. Estimate the

probability that a randomly selected member earns at least $79,000. Round your answers to thenearest tenth.

89,000 99,000 69,000 104,000 74,000 89,000 79,000 59,000 114,000 139,000 64,000 84,000 109,00074,000 99,000 94,000 79,000 119,000 54,000 94,000

23)

A) 0.4 B) 0.7 C) 0.8 D) 0.6

24) Of 1085 people who came into a blood bank to give blood, 340 people had high blood pressure.Estimate the probability that the next person who comes in to give blood will have high bloodpressure.

24)

A) 0.313 B) 0.232 C) 0.281 D) 0.364

25) In a certain class of students, there are 10 boys from Wilmette, 5 girls from Winnetka, 8 girls fromWilmette, 5 boys from Glencoe, 3 boys from Winnetka and 8 girls from Glenoce. If the teachercalls upon a student to answer a question, what is the probability that the student will be a boy?

25)

A) 0.742 B) 0.256 C) 0.462 D) 0.385

From the information provided, create the sample space of possible outcomes.26) Flip a coin three times. 26)

A) HHH HHT HTH HTT THH THT TTH TTTB) HTT THT HTH HHH TTH TTTC) HHH TTT THT HTH HHT TTH HTHD) HHH HTT HTH TTT HTT THH HHT THT

27) Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Eachtakes out a piece and eats it. What are the possible pairs of candies eaten?

27)

A) LD-LD CD-LD LP-LP LD-LP CD-CD LD-LP LP-CD CD-LD LP-LDB) CD-LD LD-LP LP-CD LP-LP LD-LDC) LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD CD-LP LP-LDD) LD-CD LD-CD LD-CD LD-LP LD-LP LD-LP CD-LP CD-LP CD-LP

Answer the question.28) In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly

from the town, what are the odds against selecting someone who commutes by bicycle?28)

A) 1 : 3 B) 3 : 1 C) 3 : 4 D) 1 : 4

29) Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $259(including your $7 bet) if you win. Find the odds used for determining the payoff.

29)

A) 1 : 36 B) 37 : 1 C) 36 : 1 D) 259 : 266

Determine whether the events are mutally exclusive.30) Meet a man with an umbrella.

Meet a man with a raincoat.30)

A) No B) Yes

31) Get a full time day job as a teller with a bank.Get a full time day job as a cashier at a store.

31)

A) Yes B) No

3

32) Go to a formal dinner affair.Wear blue jeans.

32)

A) No B) Yes

33) Get stung by a bee.Get stung by a wasp.

33)

A) Yes B) No

Find the indicated probability.34) Find P(A), given that P(A) = 0.839. 34)

A) 0 B) 1.839 C) 1.192 D) 0.161

35) Based on meteorological records, the probability that it will snow in a certain town on January 1stis 0.455. Find the probability that in a given year it will not snow on January 1st in that town.

35)

A) 0.545 B) 2.198 C) 1.455 D) 0.835

36) The probability that Luis will pass his statistics test is 0.74. Find the probability that he will fail hisstatistics test.

36)

A) 0.26 B) 2.85 C) 1.35 D) 0.37

37) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignoreleap years.

37)

A) 1112 B) 334

365 C) 31334 D) 31

365

38) A spinner has equal regions numbered 1 through 21. What is the probability that the spinner willstop on an even number or a multiple of 3?

38)

A) 23 B) 10

9 C) 17 D) 13

39) If you pick a card at random from a well shuffled deck, what is the probability that you get a facecard or a spade?

39)

A) 122 B) 11

26 C) 2552 D) 9

26

40) The table below describes the smoking habits of a group of asthma sufferers.

NonsmokerOccasional

smokerRegular

smokerHeavy

smoker TotalMen 340 34 74 37 485

Women 398 39 74 50 561Total 738 73 148 87 1046

If one of the 1046 people is randomly selected, find the probability that the person is a man or aheavy smoker.

40)

A) 0.511 B) 0.476 C) 0.547 D) 0.425

4

41) Of the 68 people who answered "yes" to a question, 12 were male. Of the 87 people that answered"no" to the question, 8 were male. If one person is selected at random from the group, what is theprobability that the person answered "yes" or was male?

41)

A) 0.129 B) 0.176 C) 0.49 D) 0.568

42) A study of consumer smoking habits includes 163 people in the 18-22 age bracket (44 of whomsmoke), 140 people in the 23-30 age bracket (37 of whom smoke), and 81 people in the 31-40 agebracket (25 of whom smoke). If one person is randomly selected from this sample, find theprobability of getting someone who is age 23-30 or smokes.

42)

A) 0.641 B) 0.264 C) 0.096 D) 0.544

43) A study of consumer smoking habits includes 177 people in the 18-22 age bracket (43 of whomsmoke), 134 people in the 23-30 age bracket (30 of whom smoke), and 86 people in the 31-40 agebracket (29 of whom smoke). If one person is randomly selected from this sample, find theprobability of getting someone who is age 18-22 or does not smoke.

43)

A) 0.757 B) 1.189 C) 0.338 D) 0.851

44) 100 employees of a company are asked how they get to work and whether they work full time orpart time. The figure below shows the results. If one of the 100 employees is randomly selected,find the probability of getting someone who carpools or someone who works full time.

1. Public transportation: 9 full time, 7 part time2. Bicycle: 3 full time, 4 part time3. Drive alone: 31 full time, 28 part time4. Carpool: 9 full time, 9 part time

44)

A) 0.61 B) 0.54 C) 0.28 D) 0.14

45) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9). 45)

A) 132 B) 8 C) 2

13 D) 413

46) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4). 46)

A) 16 B) 213 C) 12

13 D) 413

5


NonsmokerOccasional

smokerRegular smoker

Heavysmoker Total

Men 328 36 80 31 475Women 340 37 60 45 482

Total 668 73 140 76 957

If one of the 957 people is randomly selected, find the probability of getting a regular or heavysmoker.

47)

A) 0.146 B) 0.116 C) 0.514 D) 0.226

48) A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. Find P(not blue). 48)

A) 13 B) 8 C) 2

3 D) 32

49) The probability that an event will occur is 0.3. What is the probability that the event will not occur? 49)

A) 0 B) 0.7

C) 37 D) None of the above is correct.

50) In one town, 31% of all voters are Democrats. If two voters are randomly selected for a survey,find the probability that they are both Democrats.

50)

A) 0.620 B) 0.096 C) 0.310 D) 0.093

51) Find the probability of correctly answering the first 2 questions on a multiple choice test if randomguesses are made and each question has 3 possible answers.

51)

A) 18 B) 1

9 C) 32 D) 2

3

52) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and30% are defective. If three of the products are randomly selected, find the probability that all ofthem are acceptable.

52)

A) 0.429 B) 0.027 C) 2.1 D) 0.343

53) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two goodcoils when two coils are randomly selected if the first selection is replaced before the second ismade.

53)

A) 0.176 B) 0.7744 C) 0.7733 D) 0.0144

54) A bin contains 77 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected fromthe bin with replacement, find the probability that all the bulbs selected are good ones.

54)

A) 0.499 B) 0.543 C) 0 D) 0.87

55) In one town, 64% of adults have health insurance. What is the probability that 6 adults selected atrandom from the town all have health insurance?

55)

A) 0.069 B) 0.64 C) 0.094 D) 3.84

6

56) A study conducted at a certain college shows that 52% of the school's graduates find a job in theirchosen field within a year after graduation. Find the probability that 9 randomly selectedgraduates all find jobs in their chosen field within a year of graduating.

56)

A) 0.173 B) 4.680 C) 0.005 D) 0.003

57) Find the probability that 2 randomly selected people all have the same birthday. Ignore leap years. 57)A) 0.0055 B) 0.00273973 C) 0.5 D) 0.00000751

Provide a written description of the complement of the given event.58) When 10 adults are tested for high blood pressure, at least one of the results are positive. 58)

A) All of the adults have high blood pressure.B) Nine of the adults have high blood pressure.C) None of the adults have high blood pressure.

59) When 100 engines are shipped, all of them are free of defects. 59)A) At least one of the engines is defective.B) None of the engines are defective.C) All of the engines are defective.

Find the indicated probability.60) An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the

probability that there is at least one correct answer.60)

A) 110 B) 1

1,024 C) 910 D) 1,023

1,024

61) A study conducted at a certain college shows that 57% of the school's graduates find a job in theirchosen field within a year after graduation. Find the probability that among 8 randomly selectedgraduates, at least one finds a job in his or her chosen field within a year of graduating.

61)

A) 0.125 B) 0.570 C) 0.989 D) 0.999

62) A sample of 4 different calculators is randomly selected from a group containing 11 that aredefective and 30 that have no defects. What is the probability that at least one of the calculators isdefective?

62)

A) 0.713 B) 0.729 C) 0.110 D) 0.271

63) In a batch of 8,000 clock radios 7% are defective. A sample of 6 clock radios is randomly selectedwithout replacement from the 8,000 and tested. The entire batch will be rejected if at least one ofthose tested is defective. What is the probability that the entire batch will be rejected?

63)

A) 0.0700 B) 0.353 C) 0.167 D) 0.647

64) In a blood testing procedure, blood samples from 6 people are combined into one mixture. Themixture will only test negative if all the individual samples are negative. If the probability that anindividual sample tests positive is 0.12, what is the probability that the mixture will test positive?

64)

A) 0.536 B) 0.00000299 C) 1.00 D) 0.0144

7

65) The table below shows the soft drinks preferences of people in three age groups. cola root beer lemon-lime

under 21 years of age 40 25 20between 21 and 40 35 20 30

over 40 years of age 20 30 35

If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years ofage.

65)

A) 13 B) 1

2 C) 35 D) 2

5




If one of the 255 subjects is randomly selected, find the probability that the person is over 40 anddrinks cola.

66)

A) 417 B) 4

51





If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years ofage given that they drink root beer.

67)

A) 517 B) 2

5





If one of the 255 subjects is randomly selected, find the probability that the person drinks root beergiven that they are over 40.

68)

A) 25 B) 6

17


8

69) The following table contains data from a study of two airlines which fly to Small Town, USA.

Number of flights which were on time

Number of flightswhich were late

Podunk Airlines 33 6Upstate Airlines 43 5

If one of the 87 flights is randomly selected, find the probability that the flight selected arrived ontime given that it was an Upstate Airlines flight.

69)

A) 1176 B) 43

87






If one of the 87 flights is randomly selected, find the probability that the flight selected is an UpstateAirlines flight given that it was late.

70)

A) 548 B) 5

87






If one of the 87 flights is randomly selected, find the probability that the flight selected is an UpstateAirlines flight which was on time.

71)

A) 4387 B) 11

76


9


Nonsmoker Lightsmoker

Heavysmoker Total

Men 362 89 60 511Women 392 61 72 525

Total 754 150 132 1036

If one of the 1036 subjects is randomly selected, find the probability that the person chosen is anonsmoker given that it is a woman. Round to the nearest thousandth.

72)

A) 0.520 B) 0.747 C) 0.378 D) 0.407


Nonsmoker Lightsmoker

Heavysmoker Total

Men 380 83 87 550Women 322 73 67 462

Total 702 156 154 1012

If one of the 1012 subjects is randomly selected, find the probability that the person chosen is awoman given that the person is a light smoker.

73)

A) 0.468 B) 0.158 C) 0.072 D) 0.254

Solve the problem.74) There are 11 members on a board of directors. If they must form a subcommittee of 3 members,

how many different subcommittees are possible?74)

A) 165 B) 1331 C) 6 D) 990

75) The library is to be given 7 books as a gift. The books will be selected from a list of 19 titles. If eachbook selected must have a different title, how many possible selections are there?

75)

A) 2.413593262e+13 B) 50,388C) 1.216451004e+17 D) 253,955,520

76) How many ways can an IRS auditor select 4 of 10 tax returns for an audit? 76)A) 210 B) 10,000 C) 24 D) 5040

77) A state lottery involves the random selection of six different numbers between 1 and 21. If youselect one six number combination, what is the probability that it will be the winning combination?

77)

A) 1720 B) 1

39,070,080 C) 185,766,121 D) 1

54,264

78) 8 basketball players are to be selected to play in a special game. The players will be selected from alist of 27 players. If the players are selected randomly, what is the probability that the 8 tallestplayers will be selected?

78)

A) 827 B) 1

2,220,075 C) 140,320 D) 1

213,127,200

10

79) The organizer of a television show must select 5 people to participate in the show. The participantswill be selected from a list of 28 people who have written in to the show. If the participants areselected randomly, what is the probability that the 5 youngest people will be selected?

79)

A) 27 B) 1

11,793,600 C) 1120 D) 1

98,280

80) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits isnot allowed?

80)

A) 5 B) 6 C) 210 D) 343

81) A musician plans to perform 5 selections. In how many ways can she arrange the musicalselections?

81)

A) 5 B) 25 C) 120 D) 720

82) A pollster wants to minimize the effect the order of the questions has on a person's response to asurvey. How many different surveys are required to cover all possible arrangements if there are 6questions on the survey?

82)

A) 6 B) 720 C) 120 D) 36

83) There are 7 members on a board of directors. If they must elect a chairperson, a secretary, and atreasurer, how many different slates of candidates are possible?

83)

A) 343 B) 35 C) 210 D) 5040

84) A tourist in France wants to visit 12 different cities. How many different routes are possible? 84)A) 144 B) 12 C) 479,001,600 D) 39,916,800

85) A tourist in France wants to visit 11 different cities. If the route is randomly selected, what is theprobability that she will visit the cities in alphabetical order?

85)

A) 139,916,800 B) 1

121 C) 39,916,800 D) 111

86) In a certain lottery, five different numbers between 1 and 31 inclusive are drawn. These are thewinning numbers. To win the lottery, a person must select the correct 5 numbers in the same orderin which they were drawn. What is the probability of winning?

86)

A) 1120 B) 1

31! C) 120,389,320 D) 120

20,389,320

Identify the given random variable as being discrete or continuous.87) The number of oil spills occurring off the Alaskan coast 87)

A) Discrete B) Continuous

88) The pH level in a shampoo 88)A) Continuous B) Discrete

11

Find the mean of the given probability distribution.89)

x P(x)0 0.191 0.112 0.303 0.064 0.34

89)

A) 2.34 B) 2.15 C) 2.44 D) 2.25

90) The number of golf balls ordered by customers of a pro shop has the following probabilitydistribution.

x 3 6 9 12 15p(x) 0.14 0.28 0.36 0.12 0.10

90)

A) 5.61 B) 9 C) 9.24 D) 8.28

91) In a certain town, 30% of adults have a college degree. The accompanying table describes theprobability distribution for the number of adults (among 4 randomly selected adults) who have acollege degree. x P(x)0 0.24011 0.41162 0.26463 0.07564 0.0081

91)

A) 1.20 B) 1.44 C) 2.00 D) 1.10

92) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Round answer to the nearest hundredth.

92)

A) 0.62 B) 2.00 C) 0.72 D) 1.17

93) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in agiven day are 0.50, 0.43, 0.06, and 0.01, respectively.

93)

A) 1.50 B) 0.58 C) 0.25 D) 1.08

Solve the problem.94) In a game, you have a 1/29 probability of winning $106 and a 28/29 probability of losing $9. What

is your expected value?94)

A) -$5.03 B) $3.66 C) -$8.69 D) $12.34

95) A contractor is considering a sale that promises a profit of $35,000 with a probability of 0.7 or a loss(due to bad weather, strikes, and such) of $6000 with a probability of 0.3. What is the expectedprofit?

95)

A) $28,700 B) $24,500 C) $29,000 D) $22,700

96) Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 forrolling a 6 or a 5, nothing otherwise. What is your expected value?

96)

A) $4.00 B) $2.00 C) -$0.67 D) -$2.00

12

97) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winningticket is to be $500. What is your expected value?

97)

A) -$0.40 B) -$1.00 C) $0.00 D) -$0.50

98) The prizes that can be won in a sweepstakes are listed below together with the chances of winningeach one:$4800 (1 chance in 8300); $1700 (1 chance in 5300); $900 (1 chance in 4600);$300 (1 chance in 2700).Find the expected value of the amount won for one entry if the cost of entering is 65 cents.

98)

A) $1.09 B) $0.52 C) $300 D) $0.56

99) The prizes that can be won in a sweepstakes are listed below together with the chances of winningeach one:$5300 (1 chance in 8100); $2000 (1 chance in 6000); $500 (1 chance in 4400);$100 (1 chance in 2300).Find the expected value of the amount won for one entry if the cost to enter is 61 cents.

99)

A) $99.39 B) $1.14 C) $0.49 D) $0.53

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. Theprobabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question usingthe table.

Probabilities of Girlsx(girls) P(x) x(girls) P(x) x(girls) P(x)

0 0.000 5 0.122 10 0.0611 0.001 6 0.183 11 0.0222 0.006 7 0.209 12 0.0063 0.022 8 0.183 13 0.0014 0.061 9 0.122 14 0.000

100) Find the probability of selecting exactly 8 girls. 100)A) 0.022 B) 0.183 C) 0.000 D) 0.122



103) Find the probability of selecting 9 or more girls. 103)A) 0.212 B) 0.001 C) 0.061 D) 0.122



13

Answer the question.106) Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30

probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30probability that it will last seven games. Is it unusual for a team to win a series in 5 games?

106)

A) No B) Yes

107) Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

107)

A) No B) Yes

108) Suppose that computer literacy among people ages 40 and older is being studied and that theaccompanying tables describes the probability distribution for four randomly selected people,where x is the number that are computer literate. Is it unusual to find four computer literatesamong four randomly selected people?

x P x0 0.161 0.252 0.363 0.154 0.08

108)

A) No B) Yes

109) Suppose that voting in municipal elections is being studied and that the accompanying tablesdescribes the probability distribution for four randomly selected people, where x is the number thatvoted in the last election. Is it unusual to find four voters among four randomly selected people?

x P x0 0.231 0.322 0.263 0.154 0.04

109)

A) Yes B) No

110) Suppose that a law enforcement group studying traffic violations determines that theaccompanying table describes the probability distribution for five randomly selected people,where x is the number that have received a speeding ticket in the last 2 years. Is it unusual to findno speeders among five randomly selected people?

x P x0 0.081 0.182 0.253 0.224 0.195 0.08

110)

A) Yes B) No

14

Find the indicated probability.111) A test consists of 10 true/false questions. To pass the test a student must answer at least 8 questions

correctly. If a student guesses on each question, what is the probability that the student will passthe test?

111)

A) 0.044 B) 0.989 C) 0.055 D) 0.011

112) A machine has 11 identical components which function independently. The probability that acomponent will fail is 0.2. The machine will stop working if more than three components fail. Findthe probability that the machine will be working.

112)

A) 0.949 B) 0.111 C) 0.162 D) 0.839

113) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students areselected at random from the physics majors, that is the probability that no more than 6 belong toan ethnic minority?

113)

A) 0.9815 B) 0.0547 C) 0.913 D) 0.9846

114) Find the probability of at least 2 girls in 9 births. Assume that male and female births are equallylikely and that the births are independent events.

114)

A) 0.980 B) 0.070 C) 0.020 D) 0.910

115) A company purchases shipments of machine components and uses this acceptance sampling plan:Randomly select and test 26 components and accept the whole batch if there are fewer than 3defectives. If a particular shipment of thousands of components actually has a 3% rate of defects,what is the probability that this whole shipment will be accepted?

115)

A) 0.0348 B) 0.9580 C) 0.5051 D) 0.1408

116) An airline estimates that 92% of people booked on their flights actually show up. If the airlinebooks 75 people on a flight for which the maximum number is 73, what is the probability that thenumber of people who show up will exceed the capacity of the plane?

116)

A) 0.0548 B) 0.0019 C) 0.0145 D) 0.0125

117) In a study, 40% of adults questioned reported that their health was excellent. A researcher wishesto study the health of people living close to a nuclear power plant. Among 10 adults randomlyselected from this area, only 3 reported that their health was excellent. Find the probability thatwhen 10 adults are randomly selected, 3 or fewer are in excellent health.

117)

A) 0.2150 B) 0.2687 C) 0.1673 D) 0.3823

118) The participants in a television quiz show are picked from a large pool of applicants withapproximately equal numbers of men and women. Among the last 10 participants there have beenonly 2 women. If participants are picked randomly, what is the probability of getting 2 or fewerwomen when 10 people are picked?

118)

A) 0.0439 B) 0.0107 C) 0.0537 D) 0.0547

119) A car insurance company has determined that 8% of all drivers were involved in a car accident lastyear. Among the 15 drivers living on one particular street, 3 were involved in a car accident lastyear. If 15 drivers are randomly selected, what is the probability of getting 3 or more who wereinvolved in a car accident last year?

119)

A) 0.1130 B) 0.9143 C) 0.0857 D) 0.3993

15

Solve the problem.120) According to a college survey, 22% of all students work full time. Find the mean for the number of

students who work full time in samples of size 16.120)

A) 0.22 B) 3.52 C) 4.00 D) 2.75

121) A die is rolled 9 times and the number of times that two shows on the upper face is counted. If thisexperiment is repeated many times, find the mean for the number of twos.

121)

A) 3 B) 2.25 C) 1.5 D) 7.5

122) On a multiple choice test with 21 questions, each question has four possible answers, one of whichis correct. For students who guess at all answers, find the mean for the number of correct answers.

122)

A) 5.3 B) 15.8 C) 7 D) 10.5

123) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 16.Find the mean for the number of seeds germinating in each batch.

123)

A) 11.36 B) 14.4 C) 11.2 D) 4.8

124) A company manufactures batteries in batches of 5 and there is a 3% rate of defects. Find the meannumber of defects per batch.

124)

A) 0.15 B) 0.155 C) 4.85 D) 0.145

125) The probability that a person has immunity to a particular disease is 0.2. Find the mean numberwho have immunity in samples of size 16.

125)

A) 0.2 B) 12.8 C) 8.0 D) 3.2

126) The probability is 0.2 that a person shopping at a certain store will spend less than $20. For groupsof size 13, find the mean number who spend less than $20.

126)

A) 10.4 B) 16.0 C) 4.0 D) 2.6

127) In a certain town, 90 percent of voters are in favor of a given ballot measure and 10 percent areopposed. For groups of 220 voters, find the mean for the number who oppose the measure.

127)

A) 22 B) 90 C) 10 D) 198

128) The probability of winning a certain lottery is 1/60,547. For people who play 973 times, find themean number of wins.

128)

A) 0.000017 B) 0.0010 C) 62.2 D) 0.0161

129) According to a college survey, 22% of all students work full time. Find the standard deviation forthe number of students who work full time in samples of size 16.

129)

A) 1.88 B) 2.75 C) 1.66 D) 3.52

130) A die is rolled 6 times and the number of twos that come up is tallied. If this experiment isrepeated many times, find the standard deviation for the number of twos.

130)

A) 0.833 B) 0.917 C) 0.913 D) 1.22

131) On a multiple choice test with 16 questions, each question has four possible answers, one of whichis correct. For students who guess at all answers, find the standard deviation for the number ofcorrect answers.

131)

A) 1.732 B) 1.677 C) 1.643 D) 1.697

16

132) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 5.Find the standard deviation for the number of seeds germinating in each batch.

132)

A) 1.025 B) 0.917 C) 0.906 D) 1.012

133) A company manufactures batteries in batches of 11 and there is a 3% rate of defects. Find thestandard deviation for the number of defects per batch.

133)

A) 0.566 B) 0.574 C) 0.564 D) 0.539

134) On a multiple choice test with 12 questions, each question has four possible answers, one of whichis correct. For students who guess at all answers, find the variance for the number of correctanswers.

134)

A) 2.16 B) 2.25 C) 1.98 D) 2.063

135) A company manufactures batteries in batches of 18 and there is a 3% rate of defects. Find thevariance for the number of defects per batch.

135)

A) 0.524 B) 0.52 C) 0.495 D) 0.54

136) The probability of winning a certain lottery is 1/78,059. For people who play 955 times, find thestandard deviation for the number of wins.

136)

A) 0.1106 B) 0.1212 C) 0.0122 D) 3.4181

137) In a certain town, 56% of voters favor a given ballot measure. For groups of 35 voters, find thevariance for the number who favor the measure.

137)

A) 74.37 B) 2.94 C) 8.62 D) 19.60

Using the following uniform density curve, answer the question.

138) What is the probability that the random variable has a value greater than 4? 138)A) 0.450 B) 0.375 C) 0.500 D) 0.625

139) What is the probability that the random variable has a value greater than 1.4? 139)A) 0.9500 B) 0.8250 C) 0.7750 D) 0.7000

140) What is the probability that the random variable has a value less than 8? 140)A) 1.000 B) 0.750 C) 1.125 D) 0.875

141) What is the probability that the random variable has a value less than 4.1? 141)A) 0.5125 B) 0.2625 C) 0.3875 D) 0.6375

142) What is the probability that the random variable has a value between 4.4 and 4.7? 142)A) 0.0875 B) 0.1625 C) 0.0375 D) 0.2875

17

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spreadevenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range ofpounds lost.

143) Between 10.5 pounds and 12 pounds 143)

A) 14 B) 1

2 C) 34 D) 1

3

If Z is a standard normal variable, find the probability.144) The probability that Z lies between 0 and 3.01 144)

A) 0.5013 B) 0.1217 C) 0.4987 D) 0.9987

145) The probability that Z lies between -2.41 and 0 145)A) 0.4920 B) 0.5080 C) 0.0948 D) 0.4910

146) The probability that Z is less than 1.13 146)A) 0.8485 B) 0.1292 C) 0.8907 D) 0.8708

147) The probability that Z lies between -1.10 and -0.36 147)A) 0.2237 B) -0.2237 C) 0.4951 D) 0.2239

148) The probability that Z lies between 0.7 and 1.98 148)A) 0.2181 B) -0.2181 C) 1.7341 D) 0.2175

149) The probability that Z lies between -0.55 and 0.55 149)A) 0.4176 B) -0.4176 C) -0.9000 D) 0.9000

150) The probability that Z is greater than -1.82 150)A) 0.4656 B) 0.0344 C) 0.9656 D) -0.0344

151) P(Z > 0.59) 151)A) 0.2224 B) 0.7224 C) 0.2190 D) 0.2776

152) P(Z < 0.97) 152)A) 0.8078 B) 0.8315 C) 0.8340 D) 0.1660

153) P(-0.73 < Z < 2.27) 153)A) 0.2211 B) 0.4884 C) 1.54 D) 0.7557

18

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C atthe freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water,some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positivenumbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume thatthe frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected andtested. Find the temperature reading corresponding to the given information.

154) Find P96, the 96th percentile. 154)A) 1.82° B) 1.03° C) -1.38° D) 1.75°

155) Find P40, the 40th percentile. 155)A) 0.25° B) -0.25° C) 0.57° D) -0.57°

156) Find Q3, the third quartile. 156)A) 0.67° B) 0.53° C) -1.3° D) 0.82°

157) If 9% of the thermometers are rejected because they have readings that are too high, but all otherthermometers are acceptable, find the temperature that separates the rejected thermometers fromthe others.

157)

A) 1.26° B) 1.39° C) 1.45° D) 1.34°

158) If 7% of the thermometers are rejected because they have readings that are too low, but all otherthermometers are acceptable, find the temperature that separates the rejected thermometers fromthe others.

158)

A) -1.26° B) -1.39° C) -1.53° D) -1.48°

159) A quality control analyst wants to examine thermometers that give readings in the bottom 4%.Find the reading that separates the bottom 4% from the others.

159)

A) -1.63° B) -1.48° C) -1.75° D) -1.89°

160) A quality control analyst wants to examine thermometers that give readings in the bottom 7%.Find the reading that separates the bottom 7% from the others.

160)

A) -1.75° B) -1.63° C) -1.89° D) -1.48°

161) If 6.3% of the thermometers are rejected because they have readings that are too high and another6.3% are rejected because they have readings that are too low, find the two readings that are cutoffvalues separating the rejected thermometers from the others.

161)

A) -1.45° , 1.45° B) -1.53° , 1.53° C) -1.39° , 1.39° D) -1.46° , 1.46°

Solve the problem.162) In one region, the September energy consumption levels for single-family homes are found to be

normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find P45,which is the consumption level separating the bottom 45% from the top 55%.

162)

A) 1087.8 B) 1078.3 C) 1148.1 D) 1021.7

163) Scores on a test are normally distributed with a mean of 63.7 and a standard deviation of 10.3. FindP81, which separates the bottom 81% from the top 19%.

163)

A) 72.8 B) 66.7 C) 0.88 D) 0.291

19

164) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a meanof 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from thetop 40%.

164)

A) 211.3 B) 187.5 C) 207.8 D) 212.5

165) The amount of rainfall in January in a certain city is normally distributed with a mean of 3.7 inchesand a standard deviation of 0.5 inches. Find the value of the quartile Q1.

165)

A) 3.4 B) 0.9 C) 3.5 D) 4.0

166) Assume that women have heights that are normally distributed with a mean of 63.6 inches and astandard deviation of 2.5 inches. Find the value of the quartile Q3.

166)

A) 66.1 inches B) 64.3 inches C) 65.3 inches D) 67.8 inches

167) Scores on an English test are normally distributed with a mean of 30.6 and a standard deviation of6. Find the score that separates the top 59% from the bottom 41%

167)

A) 27.1 B) 29.2 C) 32.0 D) 34.1

168) Suppose that replacement times for washing machines are normally distributed with a mean of 8.6years and a standard deviation of 1.6 years. Find the replacement time that separates the top 18%from the bottom 82%.

168)

A) 8.9 years B) 10.1 years C) 9.5 years D) 7.1 years

169) Human body temperatures are normally distributed with a mean of 98.20°F and a standarddeviation of 0.62°F. Find the temperature that separates the top 7% from the bottom 93%.

169)

A) 97.28°F B) 98.78°F C) 98.40°F D) 99.12°F

170) The weights of certain machine components are normally distributed with a mean of 8.04 g and astandard deviation of 0.08 g. Find the two weights that separate the top 3% and the bottom 3%.Theses weights could serve as limits used to identify which components should be rejected.

170)

A) 7.87 g and 8.26 g B) 8.03 g and 8.05 gC) 7.89 g and 8.19 g D) 8.00 g and 8.08 g

171) The serum cholesterol levels for men in one age group are normally distributed with a mean of 178and a standard deviation of 40.5. All units are in mg/100 mL. Find the two levels that separate thetop 9% and the bottom 9%.

171)

A) 161.4 mg/100mL and 194.6 mg/100mL B) 107.5 mg/100mL and 248.5 mg/100mLC) 165.0 mg/100mL and 190.96 mg/100mL D) 123.7 mg/100mL and 232.3 mg/100mL

Find the indicated probability.172) The diameters of bolts produced by a certain machine are normally distributed with a mean of

0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diametergreater than 0.32 inches?

172)

A) 2.28% B) 47.72% C) 97.72% D) 37.45%

173) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and astandard deviation $150. What percentage of trainees earn less than $900 a month?

173)

A) 9.18% B) 90.82% C) 35.31% D) 40.82%

20

174) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and astandard deviation of 1.2 oz. What is the probability that the volume of soda in a randomlyselected bottle will be less than 32 oz?

174)

A) 0.3821 B) 0.0987 C) 0.5987 D) 0.4013

175) The diameters of pencils produced by a certain machine are normally distributed with a mean of0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of arandomly selected pencil will be less than 0.285 inches?

175)

A) 0.0596 B) 0.4332 C) 0.9332 D) 0.0668

176) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and astandard deviation of $45. What is the probability that a randomly selected teacher earns morethan $525 a week?

176)

A) 0.1003 B) 0.2823 C) 0.2177 D) 0.7823

177) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a meanof 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of arating that is between 200 and 275.

177)

A) 0.5 B) 0.9332 C) 0.4332 D) 0.0668

178) In one region, the September energy consumption levels for single-family homes are found to benormally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For arandomly selected home, find the probability that the September energy consumption level isbetween 1100 kWh and 1225 kWh.

178)

A) 0.0910 B) 0.3791 C) 0.1971 D) 0.2881

179) The lengths of human pregnancies are normally distributed with a mean of 268 days and astandard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

179)

A) 0.4834 B) 0.0166 C) 0.9834 D) 0.0179

180) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standarddeviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g.What percentage of legal quarters will be rejected?

180)

A) 0.0196% B) 1.62% C) 1.96% D) 2.48%

Solve the problem.181) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of

89 inches, and a standard deviation of 16 inches. What is the probability that the mean annualsnowfall during 64 randomly picked years will exceed 91.8 inches?

181)

A) 0.4192 B) 0.0026 C) 0.5808 D) 0.0808

182) The annual precipitation amounts in a certain mountain range are normally distributed with amean of 99 inches, and a standard deviation of 14 inches. What is the probability that the meanannual precipitation during 49 randomly picked years will be less than 101.8 inches?

182)

A) 0.5808 B) 0.0808 C) 0.9192 D) 0.4192

183) The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and astandard deviation of 12. If 16 fish are randomly selected, what is the probability that the meanweight will be between 8.6 and 14.6 lb?

183)

A) 0.3270 B) 0.6730 C) 0.0968 D) 0.4032

21

184) The scores on a certain test are normally distributed with a mean score of 65 and a standarddeviation of 2. What is the probability that a sample of 90 students will have a mean score of atleast 65.2108?

184)

A) 0.1587 B) 0.3174 C) 0.3413 D) 0.8413

185) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a meanof 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find theprobability that their mean is above 215.

185)

A) 0.1179 B) 0.3821 C) 0.0287 D) 0.4713

186) In one region, the September energy consumption levels for single-family homes are found to benormally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. If 50different homes are randomly selected, find the probability that their mean energy consumptionlevel for September is greater than 1075 kWh.

186)

A) 0.2910 B) 0.4562 C) 0.2090 D) 0.0438

187) Assume that women's heights are normally distributed with a mean of 63.6 inches and a standarddeviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have amean height between 62.9 inches and 64.0 inches.

187)

A) 0.0424 B) 0.7248 C) 0.1739 D) 0.9318

188) Suppose that replacement times for washing machines are normally distributed with a mean of9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selectedwashing machines will have a mean replacement time less than 9.1 years.

188)

A) 0.4286 B) 0.0643 C) 0.4357 D) 0.0714

189) Human body temperatures are normally distributed with a mean of 98.20°F and a standarddeviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean bodytemperature will be less than 98.50°F.

189)

A) 0.3343 B) 0.0833 C) 0.9826 D) 0.4826

190) For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a meanof 114.8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find theprobability that their mean systolic blood pressure is between 119 and 122.

190)

A) 0.0577 B) 0.3343 C) 0.0833 D) 0.9341

191) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 ChevroletCavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanicsare randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.

191)

A) 0.1946 B) 0.1285 C) 0.1346 D) 0.1469


192)

A) 0.1046 B) 0.1285 C) 0.0069 D) 0.0046


193)

A) 0.8531 B) 0.9931 C) 0.9712 D) 0.9634

22


194)

A) 0.8531 B) 0.7285 C) 0.8457 D) 0.9146

195) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 ChevroletCavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanicsare randomly selected, find the probability that their mean rebuild time is less than 7.6 hours.

195)

A) 0.0103 B) 0.0008 C) 0.0036 D) 0.0025

196) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 ChevroletCavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanicsare randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.

196)

A) 0.9589 B) 0.9756 C) 0.4276 D) 0.9608

197) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students arerandomly selected, find the probability that the mean of their test scores is greater than 78.

197)

A) 0.0103 B) 0.8962 C) 0.0036 D) 0.0008

198) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students arerandomly selected, find the probability that the mean of their test scores is greater than 71.

198)

A) 0.5036 B) 0.0008 C) 0.8962 D) 0.9012

199) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students arerandomly selected, find the probability that the mean of their test scores is less than 76.

199)

A) 0.8962 B) 0.9203 C) 0.9699 D) 0.0301

200) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students arerandomly selected, find the probability that the mean of their test scores is less than 70.

200)

A) 0.9699 B) 0.0301 C) 0.0278 D) 0.1006

23

EXTRA CREDIT: Answer questions on a seperate paper.Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.

201) A multiple choice test consists of 60 questions. Each question has 4 possible answers ofwhich one is correct. If all answers are random guesses, estimate the probability of gettingat least 20% correct.

201)

202) A certain question on a test is answered correctly by 22% of the respondents. Estimate theprobability that among the next 150 responses there will be at most 40 correct answers.

202)

203) A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimatethe probability that a randomly selected batch contains more than 6 defects.

203)

204) In one county, the conviction rate for speeding is 85%. Estimate the probability that of thenext 100 speeding summonses issued, there will be at least 90 convictions.

204)

205) The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140randomly selected seeds, exactly 100 will germinate.

205)

206) Two percent of hair dryers produced in a certain plant are defective. Estimate theprobability that of 10,000 randomly selected hair dryers, exactly 225 are defective.

206)

207) Two percent of hair dryers produced in a certain plant are defective. Estimate theprobability that of 10,000 randomly selected hair dryers, at least 219 are defective.

207)

208) A coin is tossed 20 times. A person, who claims to have extrasensory perception, is askedto predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What isthe probability of being correct 14 or more times by guessing? Does this probability seemto verify her claim?

208)

209) Find the probability that in 200 tosses of a fair die, we will obtain at exactly 30 fives. 209)

210) Merta reports that 74% of its trains are on time. A check of 60 randomly selected trainsshows that 38 of them arrived on time. Find the probability that among the 60 trains, 38 orfewer arrive on time. Based on the result, does it seem plausible that the "on-time" rate of74% could be correct?

210)

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Documents

Ch. 4, 5, 6 Name___________________________________ 03/24/2010 Math 227 Exam #2