PDF Math110 Practice Final Exam Fall 2009[1]

Math 110 Practice Final ExamFall 2009

Covers 5.1-5.3, 6.1-6.4, 7.1-7.5, 8.1-8.4, 9.1-9.3

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

Find the simple interest. Assume a 360-day year. Round results to the nearest cent.

1) $15,612 at 8.6% for 9 months

A) $895.09 B) $1006.97 C) $1118.86 D) $1015.44

1)

2) $13,000 at 3% for 95 days

A) $390.00 B) $102.92 C) $101.83 D) $13,102.92

2)

Find the compound amount for the deposit. Round to the nearest cent.

3) $16,000 at 8% compounded annually for 8 years

A) $29,614.88 B) $26,240.00 C) $27,421.19 D) $24,960.00

3)

4) $1200 at 8% compounded quarterly for 2 years

A) $1248.48 B) $1392.00 C) $1399.68 D) $1405.99

4)

Find the amount that should be invested now to accumulate the following amount, if the money is compounded as

indicated.

5) $8200 at 8% compounded annually for 11 years.

A) $3798.19 B) $3516.84 C) $4683.16 D) $19,119.44

5)

6) $6000 at 6.7% compounded semiannually for 6 years

A) $4065.98 B) $4040.41 C) $8909.99 D) $1959.59

6)

Solve the problem.

7) Barbara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then.

How much should she invest now at 8%, compounded quarterly, so that she will have enough to

buy a new car?

A) $12,860.08 B) $11,025.45 C) $13,334.95 D) $11,827.40

7)

8) Andrea Gilford's savings account has a balance of $3430. After 3 years, what will the amount of

interest be at 2% compounded quarterly?

A) $202.55 B) $211.55 C) $34.30 D) $216.55

8)

Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.

9) R = $100, i = 0.06, n = 7

A) $697.53 B) $2506.05 C) $839.38 D) $236.42

9)

10) R = $2,500, i = 6% interest compounded quarterly for 16 years

A) $259,137.01 B) $432,190.74 C) $265,524.07 D) $99,856.59

10)

1

Find the periodic payment that will render the sum.

11) S = $35,000, interest is 8% compounded annually, payments made at the end of each year for 12

years

A) $3290.52 B) $2102.67 C) $2845.60 D) $1844.33

11)

12) S = $57,000, interest is 4% compounded annually, payments made at the end of each year for

5 years

A) $10,523.75 B) $5358.84 C) $3424.35 D) $4634.26

12)

Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the

following amount. Payments are made at the end of each period. The interest rate given is per period.

13) $6400; money earns 5% compounded annually; 9 annual payments

A) $670.22 B) $580.42 C) $508.83 D) $206.27

13)

14) $89,000; money earns 8.2% compounded quarterly for 31

2 years

A) $986.59 B) $2237.66 C) $5552.97 D) $902.57

14)

Find the present value of the ordinary annuity.

15) Payments of $530 made annually for 13 years at 6% compounded annually

A) $4690.24 B) $4926.35 C) $4691.92 D) $4443.41

15)

16) Payments of $56 made quarterly for 10 years at 8% compounded quarterly

A) $1541.99 B) $1531.91 C) $1506.55 D) $549.81

16)

Find the payment necessary to amortize the loan.

17) $2500; 6% compounded annually; 7 annual payments

A) $508.41 B) $452.21 C) $402.59 D) $447.84

17)

18) $12,900; 12% compounded monthly; 48 monthly payments

A) $339.95 B) $334.30 C) $1554.74 D) $339.71

18)

Find the monthly house payment necessary to amortize the following loan.

19) $50,000 at 5.28% for 15 years

A) $14.67 B) $402.73 C) $456.05 D) $220.00

19)

20) $169,000 at 8.6% for 15 years

A) $1927.29 B) $1674.13 C) $1211.17 D) $11,923.38

20)

Write a negation for the statement.

21) x ≤ 20

A) x > 20 B) x > -20 C) ~x ≤ 20 D) x ≥ 20

21)

2

22) That athlete wants to be a musician.

A) That athlete does not want to be a musician.

B) That athlete is not a musician.

C) That musician wants to be an athlete.

D) That musician does not want to be an athlete.

22)

Translate the symbolic compound statement into words.

23) Let p represent the statement "Her name is Lisa" and let q represent the statement "She lives in

Chicago."

~p

A) Her name is Lisa. B) It is true that her name is Lisa.

C) Her name is not Lisa. D) She does not live in Chicago.

23)


Chicago."

p ∨ ~q

A) Her name is not Lisa or she lives in Chicago.

B) Her name is Lisa and she does not live in Chicago.

C) Her name is Lisa or she does not live in Chicago.

D) It is not true that her name is Lisa or she lives in Chicago.

24)


Chicago."

p ∧ q

A) Her name is Lisa and she lives in Chicago.

B) Her name is Lisa and she doesn't live in Chicago.

C) Her name is Lisa or she lives in Chicago.

D) If her name is Lisa, she lives in Chicago.

25)

Let p represent a true statement, and let q and r represent false statements. Find the truth value of the given compound

statement.

26) (p ∧ ~q) ∧ r

A) True B) False

26)

27) ~[(~p ∧ q) ∨ r]

A) False B) True

27)

Let p represent the statement 7 < 8, let q represent the statement 2 < 5 < 6, and let r represent the statement 3 < 2. Find the

truth value of the given compound statement.

28) (q ∨ ~p) ∨ ~q

A) False B) True

28)

3

Give the number of rows in the truth table for the compound statement.

29) ~(p ∨ q) ∧ (q ∧ ~r)

A) 4 B) 8 C) 9 D) 3

29)

Construct a truth table for the compound statement.

30) p ∨ ~(q ∧ c)

A)

p q c p ∨ ~(q ∧ c)

T T T T

T T F T

T F T T

T F F T

F T T F

F T F T

F F T T

F F F F

B)

p q c p ∨ ~(q ∧ c)

T T T T

T T F T

T F T T

T F F T

F T T F

F T F T

F F T T

F F F T

C)

p q c p ∨ ~(q ∧ c)

T T T T

T T F F

T F T T

T F F T

F T T F

F T F T

F F T T

F F F F

D)

p q c p ∨ ~(q ∧ c)

T T T T

T T F T

T F T T

T F F F

F T T F

F T F T

F F T T

F F F F

30)

31) (t ∧ s) ∨ (~t ∧ ~s)

A)

t s (t ∧ s) ∨ (~t ∧ ~s)

T T T

T F F

F T F

F F T

B)

t s (t ∧ s) ∨ (~t ∧ ~s)

T T T

T F F

F T T

F F T

C)

t s (t ∧ s) ∨ (~t ∧ ~s)

T T T

T F T

F T T

F F F

D)

t s (t ∧ s) ∨ (~t ∧ ~s)

T T F

T F F

F T T

F F T

31)

Use one of De Morgan's laws to write the negation of the statement.

32) The Tigers will win their sectional match or the Wolverines will win by default.

A) The Tigers will not win their sectional match or the Wolverines will not win by default.

B) The Tigers will not win their sectional match and the Wolverines will win by default.

C) The Wolverines will win by default and the Tigers will not win their sectional match.

D) The Tigers will not win their sectional match and the Wolverines will not win by default.

32)

4

33) Denim is out and linen is in.

A) Denim is not out or linen is not in. B) Denim is not out and linen is out.

C) Denim is in and linen is out. D) Denim and linen are in.

33)

Tell whether the conditional is true or false. Here T represents a true statement and F represents a false statement.

34) (2 = 2) → F

A) False B) True

34)

Let p represent "the puppy behaves well," let q represent "the puppy's owners are happy," and let r represent "the puppy

is trained." Express the compound statement in words.

35) (r ∧ p) → q

A) If the puppy is trained and the puppy behaves well, then his owners are happy.

B) If the puppy is trained, then the puppy behaves well and his owners are happy.

C) The puppy is trained and the puppy behaves well if his owners are happy.

D) If the puppy is trained or the puppy behaves well, then his owners are happy.

35)

Let p represent "I eat too much," let q represent "I exercise," and let r represent "the food is good." Write the compound

statement in symbols.

36) If I exercise, then I don't eat too much.

A) ~(p → q) B) q → ~p C) p → q D) r ∧ p

36)

Find the truth value of the statement. Assume that p and q are false, and r is true.

37) r → (~p ∨ q)

A) True B) False

37)

38) (q ∧ ~r) → (~p ∨ r)

A) True B) False

38)

Write a logical statement representing the circuit.

39)

A) p ∧ (q ∨ r) B) (p ∨ q) ∧ r C) (p ∧ q) ∧ r D) p ∨ (q ∨ r)

39)

5

40)

A) p ∧ (q ∨ r) B) p ∨ (q ∨ r) C) p ∧ q ∧ r D) (p ∨ q) ∧ r

40)

For the given direct statement, write the indicated related statement (converse, inverse, or contrapositive).

41) Love is blind. (contrapositive)

A) If it is not blind, then it is not love. B) If it is blind, then it is not love.

C) It is blind if it is love. D) If it is blind, then it is love.

41)

42) All cats catch birds. (inverse)

A) If it's not a cat, then it doesn't catch birds. B) If it catches birds, then it's a cat.

C) If it doesn't catch birds, then it's not a cat. D) Not all cats catch birds.

42)

43) ~q → ~p (contrapositive)

A) q → p B) p → q C) ~(p → q) D) ~(q → p)

43)

44) q → ~p (inverse)

A) q → p B) p → ~q C) ~q → p D) ~p → q

44)

45) If you like me, then I like you. (converse)

A) If you don't like me, then I don't like you. B) If I don't like you, then you don't like me.

C) If I like you, then you like me. D) I like you if you don't like me.

45)

Identify the statement as true or false.

46) 8 + 1 = 12 if and only if 11 = 4.

A) True B) False

46)

Tell whether the statement is true or false.

47) 8 ∈ {16, 24, 32, 40, 48}

A) True B) False

47)

48) 3 ∉ {6, 9, 12, 15, 18}

A) True B) False

48)

Insert "⊆" or "⊈" in the blank to make the statement true.

49) {3, 5, 7} {2, 3, 4, 5, 7}

A) ⊆ B) ⊈

49)

6

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement

is true or false.

50) C ⊈ B

A) True B) False

50)

Decide whether the statement is true or false.

51) {9, 18, 27, 36} ∪ {9, 27} = {9, 18, 27, 36}

A) True B) False

51)

Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of the indicated

set, using set braces.

52) A' ∪ B

A) {q, s, t, u, v, w, x, y} B) {r, s, t, u, v, w, x, z}

C) {q, r, s, t, v, x, y, z} D) {s, u, w}

52)

Shade the Venn diagram to represent the set.

53) A' ∪ B'

A) B)

C) D)

53)

7

54) A' ∪ (A ∩ B)

A) B)

C) D)

54)

8

55) (A' ∪ B) ∩ C

A) B)

C) D)

55)

Use the union rule to answer the question.

56) If n(A) = 32, n(B) = 93, and n(A ∪ B) = 109; what is n(A ∩ B)?

A) 16 B) 18 C) 48 D) 8

56)

57) If n(A) = 20, n(A ∪ B) = 58, and n(A ∩ B) = 16; what is n(B)?

A) 54 B) 38 C) 55 D) 53

57)

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.

58) n(U) = 60, n(A) = 27, n(B) = 16, and n(A ∩ B) = 3. Find n(A ∪ B)'.

A) 17 B) 40 C) 20 D) 43

58)

59) n(U) = 136, n(A) = 44, n(B) = 64, n(A ∩ B) = 17, n(A ∩ C) = 20, n(A ∩ B ∩ C) = 9, n(A' ∩ B ∩ C') = 38,

and n(A' ∩ B' ∩ C') = 33. Find n(C).

A) 41 B) 28 C) 12 D) 23

59)

9

60) n(A) = 100, n(B) = 108, n(C) = 102, n(A ∩ B) = 20, n(A ∩ C) = 22, n(B ∩ C) = 16, n(A ∩ B ∩ C) = 14,

and n(A' ∩ B' ∩ C') = 201. Find n(U)

A) 477 B) 366 C) 467 D) 266

60)

Use a Venn diagram to answer the question.

61) At East Zone University (EZU) there are 718 students taking College Algebra or Calculus. 431 are

taking College Algebra, 342 are taking Calculus, and 55 are taking both College Algebra and

Calculus. How many are taking Algebra but not Calculus?

A) 321 B) 287 C) 376 D) 663

61)

62) A survey of a group of 111 tourists was taken in St. Louis. The survey showed the following:

60 of the tourists plan to visit Gateway Arch;

45 plan to visit the zoo;

9 plan to visit the Art Museum and the zoo, but not the Gateway Arch;

13 plan to visit the Art Museum and the Gateway Arch, but not the zoo;

16 plan to visit the Gateway Arch and the zoo, but not the Art Museum;

7 plan to visit the Art Museum, the zoo, and the Gateway Arch;

16 plan to visit none of the three places.

How many plan to visit the Art Museum only?

A) 95 B) 13 C) 56 D) 32

62)

Find the probability of the given event.

63) A single fair die is rolled. The number on the die is greater than 2.

A)5

6B)

1

3C)

2

3D)

1

6

63)

64) A single fair die is rolled. The number on the die is prime.

A) 3 B)1

2C)

2

3D)

1

3

64)

Find the probability.

65) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting a

queen.

A)1

4B)

1

13C)

1

52D)

1

26

65)


club.

A)1

13B)

1

26C)

1

4D)

1

52

66)

67) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting the

4 of clubs.

A)1

13B)

1

26C)

1

4D)

1

52

67)

10


black 3 or a red 7.

A)1

4B)

1

13C)

1

26D)

1

52

68)

69) Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a

ticket at random from the box, what is the probability that you will draw 5, 9, or 3?

A)1

10B)

1

5C)

1

9D)

3

10

69)

Find the indicated probability.

70) The age distribution of students at a community college is given below.

Age (years) Number of students (f)

Under 21 416

21-25 417

26-30 211

31-35 55

Over 35 28

1127

A student from the community college is selected at random. Find the probability that the student is

at least 31. Round your answer to three decimal places.

A) 0.074 B) 0.049 C) 83 D) 0.926

70)

71) The following table shows the grades of college students in an advanced mathematics course,

broken down by year. Use the table below to find the probability that a randomly selected

sophomore gets a B.

A B C D E

Totals

(%)

Freshmen 3 5 6 4 1 19

Sophomores 6 5 8 2 3 24

Juniors 5 7 11 6 2 31

Seniors 5 4 1 4 5 19

Grad Students 3 2 2 0 0 7

Totals (%) 22 23 28 16 11 100

A)6

23B)

5

24C)

1

6D)

5

23

71)


72) A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. What is the probability that a

randomly selected marble is not blue?

A)1

3B)

2

3C)

3

2D) 8

72)

11

73) Each digit from the number 9,212,442 is written on a different card. If one of these cards is selected

at random, what is the probability of drawing a card that shows 4?

A)1

7B)

4

7C)

2

7D) 1

73)


74) Find the probability that a number less than 7 is obtained when a fair die is rolled.

A)7

6B) 0 C) 1 D)

1

6

74)

75) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either

doubles are rolled or the sum of the dice is 4.

A)1

4B)

7

36C)

2

9D)

1

36

75)

76) If you pick a card at random from a well shuffled deck, what is the probability that you get a face

card or a spade?

A)1

22B)

9

26C)

25

52D)

11

26

76)

Find the odds.

77) Find the odds in favor of drawing a number greater than 2 when a card is drawn at random from

the cards pictured below.

A) 3 to 2 B) 4 to 5 C) 4 to 1 D) 3 to 5

77)

78) Find the odds against correctly guessing the answer to a multiple choice question with 5 possible

answers.

A) 4 : 1 B) 5 : 1 C) 4 : 5 D) 5 : 4

78)


79) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.

A)1

2B) 0 C) 1 D)

1

6

79)

80) If two fair dice are rolled, find the probability of a sum of 5 given that the sum is less than 8.

A)1

6B)

2

13C)

1

9D)

4

21

80)

81) You roll two fair dice. Let E be the event that the sum is even. Let F be the event that a four shows

on at least one of the dice. Find P(F∣E).

A)5

18B)

7

18C)

1

13D)

1

3

81)

12

82) A box contains 24 blue marbles, 13 green marbles, and 13 red marbles. Two marbles are selected at

random without replacement. Let E be the event that the first marble selected is green. Let F be the

event that the second marble selected is green. Find P(F∣E) .

A)13

50B)

12

49C)

13

49D)

6

25

82)


83) Find the probability of correctly answering the first 3 questions on a multiple choice test if random

guesses are made and each question has 5 possible answers.

A)1

125B)

3

5C)

5

3D)

1

243

83)


84) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green,

and 2 red marbles. Find the probability that both marbles are green.

A)1

4B)

1

28C)

1

16D)

1

14

84)

Solve the problem.

85) 57% of a store's computers come from factory A and the remainder come from factory B. 1% of

computers from factory A are defective while 4% of computers from factory B are defective. If one

of the store's computers is selected at random, what is the probability that it is defective and from

factory B?

A) 0.47 B) 0.04 C) 0.017 D) 0.023

85)

86) 43% of a store's computers come from factory A and the remainder come from factory B. 5% of

computers from factory A are defective while 1% of computers from factory B are defective. If one

of the store's computers is selected at random, what is the probability that it is not defective and

from factory A?

A) 0.022 B) 0.409 C) 0.973 D) 0.95

86)

Use the given table to find the indicated probability.

87) 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 Totals

Cheese 13 15 20 21 69

Meat 25 21 15 13 74

Veggie 15 13 25 21 74

A student is selected at random. Find the probability that the student's favorite topping is meat

given that the student is a junior.

A) 0.069 B) 0.203 C) 0.250 D) 0.342

87)

13

88) 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 Totals

Cheese 11 12 19 19 61

Meat 22 19 12 11 64

Veggie 12 11 22 19 64

A student is selected at random. Find the probability that the student's favorite topping is veggie

given that the student is a junior or senior.

A) 0.402 B) 0.641 C) 0.415 D) 0.217

88)

Evaluate the permutation.

89) P(10, 5)

A) 720 B) 1 C) 30,240 D) 10

89)

Solve the problem.

90) Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C.

In how many ways can a person travel from A to C via B?

A) 36 ways B) 16 ways C) 10 ways D) 24 ways

90)

91) In how many ways can 4 people be chosen and arranged in a straight line, if there are 6 people

from whom to choose?


91)

92) License plates are made using 3 letters followed by 3 digits. How many plates can be made if

repetition of letters and digits is allowed?

A) 308,915,776 plates B) 1,000,000 plates

C) 1,757,600 plates D) 17,576,000 plates

92)

93) A person ordering a certain model of car can choose any of 9 colors, either manual or automatic

transmission, and any of 9 audio systems. How many ways are there to order this model of car?


93)

94) A restaurant offers 7 possible appetizers, 13 possible main courses, and 6 possible desserts. How

many different meals are possible at this restaurant? (Two meals are considered different unless all

three courses are the same).

A) 536 meals B) 26 meals C) 343 meals D) 546 meals

94)

How many distinguishable permutations of letters are possible in the word?

95) GIGGLE

A) 4320 B) 120 C) 36 D) 720

95)

14

96) TENNESSEE

A) 362,880 B) 81 C) 3780 D) 7560

96)

97) COLORADO

A) 40,320 B) 4480 C) 13,440 D) 6720

97)

Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions

with a large company. Find the number of different ways that five of these could be hired.

98) Two accounting majors must be hired first, then one economics major, then two marketing majors.


98)

99) One accounting major, one economics major, and one marketing major would be hired, then the

two remaining positions would be filled by any of the majors left.


99)

Evaluate the combination.

100)

24

1

A) 24 B) 24! C) 24! - 10 D) 2

100)

101)7

0

A) 2520 B) 5040 C) 1 D) 1260

101)

102)

19

1

A) 2 B) 19! - 10 C) 19 D) 19!

102)

103)

13

13

A) 13! - 5 B) 13! C) 1 D) 2

103)

Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain the

following cards?

104) All hearts

A) 2574 hands B) 1287 hands C) 3861 hands D) 143 hands

104)

105) Two black cards and three red cards

A) 1,690,000 hands B) 845,000 hands C) 1,267,500 hands D) 422,500 hands

105)

Solve the problem.

106) If you toss five fair coins, in how many ways can you obtain at least one head?


106)

15

107) If you toss six fair coins, in how many ways can you obtain at least two heads?


107)

108) A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many

ways can you get 5 apples?


108)

109) In how many ways can a group of 6 students be selected from 7 students?

A) 7 ways B) 6 ways C) 42 ways D) 1 way

109)

110) How many ways can a committee of 2 be selected from a club with 12 members?


110)

111) In how many ways can a group of 7 students be selected from 8 students?

A) 56 ways B) 7 ways C) 1 way D) 8 ways

111)

112) The chorus has six sopranos and eight baritones. In how many ways can the director choose a

quartet that contains at least one soprano?


112)

113) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the

committee can have at most two girls?


113)

A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the

probability.

114) All lemon

A) 0.061 B) 1 C) 0 D) 0.1212

114)

115) All orange

A) 0.0061 B) 0.0011 C) 0.0182 D) 0.7272

115)

116) 2 cherry, 1 lemon

A) 0.7272 B) 0.3636 C) 0.1818 D) 0.1212

116)

117) 1 cherry, 2 lemon

A) 0.3636 B) 0.0303 C) 0.0424 D) 0.0364

117)

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand

is made up of 13 cards.

118) In bridge, 4 aces

A) 0.00264 B) 0.00059 C) 0.00118 D) 0.01056

118)

16

119) In bridge, exactly 3 kings and exactly 3 queens

A) 0.00024 B) 0.00097 C) 0.00018 D) 0.00337

119)

Solve.

120) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice

will be greater than 10?

A) 3 B)5

18C)

1

12D)

1

18

120)

121) In a state lotto you have to pick 4 numbers from 1 to 45. If your numbers match those that the state

draws, you win. If you buy 3 tickets, what is your probability of winning?

A)1

63855B)

8

446985C)

1

148995D)

1

49665

121)

122) A lottery game contains 29 balls numbered 1 through 29. What is the probability of choosing a ball

numbered 30?

A) 0 B) 1 C)1

29D) 29

122)

Solve the problem.

123) What is the probability that at least 2 of the 435 members of the House of Representatives have the

same birthday?

A) 0.995 B) 0.996 C) 0.999 D) 1

123)

124) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people

from town C. If the council consists of 5 people, find the probability of 3 from town A and 2 from

town B.

A) 0.023 B) 0.072 C) 0.036 D) 0.076

124)

125) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people

from town C. If the council consists of 5 people, find the probability of 2 from town A, 2 from town

B, and 1 from town C.

A) 0.090 B) 0.076 C) 0.038 D) 0.189

125)

Find the requested probability.

126) A family has five children. The probability of having a girl is 1/2. What is the probability of having

exactly 3 girls and 2 boys?

A) 0.0625 B) 0.6252 C) 0.3125 D) 0.0313

126)


at least 4 girls?

A) 0.0313 B) 0.1563 C) 0.3125 D) 0.1875

127)

17


no more than 3 boys?

A) 0.3125 B) 0.5000 C) 0.8125 D) 0.9688

128)

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.

129) Exactly five twos

A) 0.083 B) 0.129 C) 0.003 D) 0.921

129)

130) Fewer than four twos

A) 0.867 B) 0.567 C) 0.364 D) 0.769

130)

131) More than one two

A) 0.005 B) 0.482 C) 0.870 D) 0.982

131)

In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from a

random sample of 10 students who are physics majors.

132) Exactly 2 belong to an ethnic minority.

A) 0.1929 B) 0.0028 C) 0.2156 D) 0.1990

132)

133) Exactly 4 do not belong to an ethnic minority.

A) 0.2564 B) 0.2253 C) 0.0467 D) 0.0547

133)

Find the probability of the event.

134) A battery company has found that the defective rate of its batteries is 0.03. Each day, 22 batteries

are randomly tested. On Tuesday, 1 is found to be defective.

A) 0.110 B) 0.614 C) 0.118 D) 0.348

134)

Find the expected value for the random variable.

135) z 3 6 9 12 15

P(z) 0.14 0.3 0.36 0.1 0.10

A) 5.49 B) 7.32 C) 8.16 D) 9.36

135)

136) A business bureau gets complaints as shown in the following table. Find the expected number of

complaints per day.

Complaints per Day 0 1 2 3 4 5

Probability 0.04 0.11 0.26 0.33 0.19 0.12

A) 2.73 B) 2.85 C) 3.01 D) 2.98

136)

18

Find the expected value for the random variable x having this probability function.

137)

x

p

x

p

a = 14 b = 15

c = 16 d = 17

A) 12.4 B) 15.5 C) 16 D) 12.7

137)

138)

x

p

x

p

a = 9 b = 11 c = 13

d = 15 e = 17

A) 13 B) 14.7 C) 16 D) 13.4

138)

Solve the problem.

139) Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3000

tickets are sold at $1.00 each, find the expected value of winning for a person who buys 1 ticket.

A) -$0.85 B) -$1.00 C) -$0.81 D) -$0.83

139)

140) Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning

ticket is to be $500. What are your expected winnings?

A) -$0.50 B) -$1.00 C) -$0.40 D) $0

140)

141) A contractor is considering a sale that promises a profit of $23,000 with a probability of 0.7 or a loss

(due to bad weather, strikes, and such) of $13,000 with a probability of 0.3. What is the expected

profit?

A) $10,000 B) $25,200 C) $16,100 D) $12,200

141)

19

Prepare a frequency distribution with a column for intervals and frequencies.

142) Use five intervals, starting with 0 - 4.

1 8 11 18 24 20 16 13 6 3 7 12 16 21 15 10 4 10 14 20

A)

Interval Frequency

0 - 4 3

5 - 9 3

10 - 14 5

15 - 19 5

20 - 24 4

B)

Interval Frequency

0 - 4 3

5 - 9 3

10 - 14 6

15 - 19 3

20 - 24 5

C)

Interval Frequency

0 - 4 3

5 - 9 2

10 - 14 7

15 - 19 4

20 - 24 4

D)

Interval Frequency

0 - 4 3

5 - 9 3

10 - 14 6

15 - 19 4

20 - 24 4

142)

143) Use five intervals, starting with 0 - 4.

2 6 12 17 21 20 17 12 5 2

8 10 19 20 16 13 5 10 15 19

A)

Interval Frequency

0 - 4 2

5 - 9 3

10 - 14 6

15 - 19 6

20 - 24 3

B)

Interval Frequency

0 - 4 2

5 - 9 4

10 - 14 4

15 - 19 7

20 - 24 3

C)

Interval Frequency

0 - 4 2

5 - 9 4

10 - 14 5

15 - 19 6

20 - 24 3

D)

Interval Frequency

0 - 4 2

5 - 9 4

10 - 14 5

15 - 19 5

20 - 24 4

143)

20

144) Use six intervals, starting with 0 - 49.

34 61 127 153 244 218 165 127 82 22 62 273

61 128 176 217 191 109 50 99 149 199 171 262

A)

Interval Frequency

0 - 49 2

50 - 99 6

100 - 149 5

150 - 199 6

200 - 249 3

250 - 299 2

B)

Interval Frequency

0 - 49 2

50 - 99 6

100 - 149 4

150 - 199 7

200 - 249 3

250 - 299 2

C)

Interval Frequency

0 - 49 2

50 - 99 5

100 - 149 6

150 - 199 6

200 - 249 3

250 - 299 2

D)

Interval Frequency

0 - 49 2

50 - 99 6

100 - 149 5

150 - 199 5

200 - 249 4

250 - 299 2

144)

Find the mean. Round to the nearest tenth.

145) Value Frequency

164 1

177 3

267 6

308 4

322 3

A) 264.4 B) 72.8 C) 307.7 D) 299.7

145)

146) Value Frequency

13 1

17 6

23 3

29 7

33 3

41 3

A) 23.3 B) 6.8 C) 29.0 D) 26.5

146)

Find the mean for the list of numbers.

147) 73, 56, 73, 93, 56 (Round to the nearest tenth, if necessary.)

A) 70.2 B) 69.7 C) 70.7 D) 87.8

147)

Find the median for the list of numbers.

148) 9, 6, 27, 16, 46, 41, 34

A) 34 B) 27 C) 26 D) 16

148)

149) 8, 5, 27, 15, 26, 46, 39, 38

A) 27 B) 26 C) 25.5 D) 26.5

149)

21

Find the indicated value for the data.

150) 17, 22, 16, 18, 15, 17, 21, 20, 13, 16, 18, 19

Find the mean. Round to the nearest tenth, if necessary.

A) 17.7 B) 17.5 C) 212 D) None of these

150)

Find the mode or modes.

151) 5, 9, 67, 3, 2, 8, 57, 1, 4, 16

A) 9 B) 8 C) 16.6 D) No mode

151)

152) 20, 45, 46, 45, 49, 45, 49

A) 42.7 B) 45 C) 49 D) No mode

152)

153) 7.4, 7.41, 7.56, 7.4, 7.88, 7.99, 7.62

A) 7.41 B) 7.609 C) 7.4 D) 7.56

153)

Find the range for the set of numbers.

154) 5, 17, 3, 14, 10

A) 3 B) 17 C) 5 D) 14

154)

155) 54, 134, 17, 106, 177

A) 17 B) 160 C) 177 D) 80

155)

Find the standard deviation for the set of numbers.

156) 6, 6, 15, 13, 12, 5, 14, 8, 7, 24

A) 5.5 B) 5.9 C) 1.2 D) 5.4

156)

157) 186, 110, 152, 205, 180, 134, 173, 279, 228

A) 54.2 B) 22.9 C) 47.8 D) 50.7

157)

Find the percent of the area under a normal curve between the mean and the given number of standard deviations from

the mean.

158) 0.83

A) 70.33% B) 29.39% C) 29.67% D) 79.67%

158)

159) -2.91

A) 99.64% B) 49.82% C) 0.18% D) 99.82%

159)

Find the percent of the total area under the standard normal curve between the given z-scores.

160) z = -1.10 and z = -0.36

A) 0.4951 B) 0.2237 C) 0.2239 D) -0.2237

160)

161) z = 0.70 and z = 1.98

A) 0.2181 B) 0.2175 C) 1.7341 D) -0.2181

161)

22

162) z = -0.55 and z = 0.55

A) 0.9000 B) 0.4176 C) -0.4176 D) -0.9000

162)

Find a z-score satisfying the given condition.

163) 20.1% of the total area is to the right of z.

A) -0.84 B) 0.82 C) 0.83 D) 0.84

163)

164) 74.9% of the total area is to the left of z.

A) 0.68 B) 0.66 C) -0.67 D) 0.67

164)

A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and

distribution approximated by a normal curve. Find the approximate number of bulbs that can be expected to last the

specified period of time.

165) At least 500 hours

A) 2500 B) 1000 C) 2400 D) 5000

165)

166) Less than 690 hours

A) 4857 B) 2357 C) 4853 D) 4860

166)

167) Between 500 hours and 675 hours

A) 4700 B) 2300 C) 4800 D) 2256

167)

168) Between 540 hours and 780 hours

A) 1710 B) 1717 C) 2217 D) 2215

168)

23

Answer KeyTestname: MATH110 PRACTICEFINALEXAMFALL 2009

1) B

2) B

3) A

4) D

5) B

6) B

7) D

8) B

9) C

10) C

11) D

12) A

13) B

14) C

15) C

16) B

17) D

18) D

19) B

20) B

21) A

22) A

23) C

24) C

25) A

26) B

27) B

28) B

29) B

30) B

31) A

32) D

33) A

34) A

35) A

36) B

37) A

38) A

39) A

40) B

41) A

42) A

43) B

44) C

45) C

46) A

47) B

48) A

49) A

50) B

24


51) A

52) C

53) B

54) D

55) A

56) A

57) A

58) C

59) A

60) C

61) C

62) B

63) C

64) B

65) B

66) C

67) D

68) B

69) D

70) A

71) B

72) B

73) C

74) C

75) C

76) D

77) A

78) A

79) B

80) D

81) A

82) B

83) A

84) B

85) C

86) B

87) C

88) A

89) C

90) D

91) B

92) D

93) B

94) D

95) B

96) C

97) D

98) B

99) D

100) A

25


101) C

102) C

103) C

104) B

105) B

106) C

107) D

108) D

109) A

110) B

111) D

112) D

113) B

114) C

115) A

116) C

117) D

118) A

119) B

120) C

121) D

122) A

123) D

124) D

125) D

126) C

127) D

128) C

129) B

130) B

131) C

132) D

133) D

134) D

135) C

136) D

137) C

138) D

139) D

140) A

141) D

142) D

143) C

144) A

145) A

146) D

147) A

148) B

149) D

150) A

26


151) D

152) B

153) C

154) D

155) B

156) B

157) D

158) C

159) B

160) B

161) A

162) B

163) D

164) D

165) A

166) A

167) B

168) A

27

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