1. The volume of liquid in an unopened 1- gallon can of paint is
an example of _________.

a) the binomial distribution

b) both discrete and continuous variable c) a continuous
random variable

d) a discrete random variable

e) a constant

2. The number of defective parts in a lot of 25 parts is an
example of _______.

a) a discrete random variable

b) a continuous random variable c) the Poisson distribution

d) the normal distribution

e) a constant

A market research team compiled the following discrete
probability distribution. In

this distribution, x represents the number of automobiles
owned by a family.

Answer questions 3-5 based on the above discrete probability
distribution.

x

P(x)

0 0.10

1 0.10

2 0.50

3 0.30

3. The mean (average) value of x is _____.

a) 1.0 b) 1.5 c) 2.0 d) 2.5 e) 3.0

4. The standard deviation of x is ________.

a) 0.80 b) 0.89 c) 1.00 d) 2.00 e) 2.25

5. Which of the following statements is true?

a) This distribution is skewed to the right. b) This is a
binomial distribution.

c) This is a normal distribution.

d) This distribution is skewed to the left. e) This
distribution is bimodal.

6. Twenty five items are randomly selected from a batch of
1000 items. Each of these

items has the same probability of being defective. The
probability that exactly 2 of

the 25 are defective could best be found by _______.

a) using the normal distribution

b) using the binomial distribution

c) using the Poisson distribution

d) using the exponential distribution e) using the uniform
distribution

7. A fair coin is tossed 5 times. What is the probability
that exactly 2 heads are

observed?

a) 0.313 b) 0.073 c) 0.400 d) 0.156 e) 0.250

Pinky Bauer, Chief Financial Officer of Harrison Haulers,
Inc., suspects irregularities

in the payroll system, and orders an inspection of a random
sample of vouchers

issued since January 1, 2006. A sample of ten vouchers is
randomly selected,

without replacement, from the population of 2,000 vouchers.
Each voucher in the

sample is examined for errors and the number of vouchers in
the sample with errors

is denoted by x.

Answer questions 8-11 based on the above information.

8. If 20% of the population of vouchers contain errors, P(x =
0) is _____________.

a) 0.8171 b) 0.1074 c) 0.8926 d) 0.3020 e) 0.2000

9. If 20% of the population of vouchers contain errors, P(x
> 0) is _____________.

a) 0.8171 b) 0.1074 c) 0.8926 d) 0.3020 e) 1.0000

10. If 20% of the population of vouchers contains errors, the
mean value of x is ____.

a) 400 b) 2 c) 200 d) 5 e) 1

11. If 20% of the population of vouchers contains errors, the
standard deviation of x

is ______.

a) 1.26 b) 1.60 c) 14.14 d) 3.16 e) 0.00

12. If x is a binomial random variable with n=8 and p=0.6,
what is the probability

that x is equal to 4?

a) 0.500 b) 0.005 c) 0.124 d) 0.232 e) 0.578

13. If x is a binomial random variable with n = 12 and p =
0.45, P(4 ≤ x ≤ 6) is _______?

a) 0.1700 b) 0.2225 c) 0.2124 d) 0.5838 e) 0.6048

14. If x is n=10 and

a) 0.6177 b) 0.2508 c) 0.3823 d) 0.6331 e) 0.3669

15. If x is n=20 and

a) 0.0654 b) 0.2277 c) 0.8867 d) 0.1144 e) 0.1133

16. If x is n=20 and

a) 0.0867 b) 0.0432 c) 0.1330 d) 0.8670 e) 0.0898

a binomial random variable with p=0.6, P(x ≥ 6) is _______?

a binomial random variable with p=0.3, P(x > 8) is
_______?

a binomial random variable with p=0.9, P(x ≤ 16) is _______?

According to Cerulli Associates of Boston, 30% of all CPA
financial advisors have an

average client size between $500,000 and $1 million.
Thirty-four percent have an

average client size between $1 million and $5 million.
Suppose a complete list of all

CPA financial advisors is available and 18 are randomly
selected from that list.

Answer the questions 17-22 based on the above information.

17. What is the expected number of CPA financial advisors
that have an average

client size between $500,000 and $1 million?

a) 0.30 b) 0.612 c) 6.12 d) 5.40 e) 0.54

18. What is the expected number with an average client size
between $1 million and

$5 million?

a) 0.34 b) 6.12 c) 0.612 d) 5.40 e) 0.54

19. What is the probability that at least eight CPA financial
advisors have an average

client size between $500,000 and $1 million?

a) 0.1407 b) 0.0811 c) 0.0596 d) 0.9404 e) 0.8593

20. What is the probability that two, three, or four CPA
financial advisors have an

average client size between $1 million and $5 million?

a) 0.0229 b) 0.0630 c) 0.1217 d) 0.7924 e) 0.2076

21. What is the probability that none of the CPA financial
advisors have an average

client size between $500,000 and $1 million?

a) 0.0006 b) 0.9994 c) 0.0016 d) 0.0084 e) 0.0126

22. What is the probability that none have an average client
size between $1 million

and $5 million?

a) 0.0016 b) 0.9994 c) 0.0084 d) 0.0006 e) 0.0126

23. The number of cars arriving at a toll booth in
five-minute intervals is Poisson

distributed with a mean of 3 cars arriving in five-minute
time intervals. The

probability of 5 cars arriving over a five-minute interval is
_______.

a) 0.0940 b) 0.0417 c) 0.1500 d) 0.1008 e) 0.2890

24. The number of cars arriving at a toll booth in
five-minute intervals is Poisson

distributed with a mean of 3 cars arriving in five-minute
time intervals. The

probability of 3 cars arriving over a five-minute interval is
_______.

a) 0.2700 b) 0.0498 c) 0.2240 d) 0.0001 e) 0.0020

25. Suppose that, for every lot of 100 computer chips a
company produces, an

average of 1.4 are defective. Another company buys many lots
of these chips at a

time, from which one lot is selected randomly and tested for
defects. If the tested lot

contains more than three defects, the buyer will reject all
the lots sent in that batch.

What is the probability that the buyer will accept the lots?
Assume that the defects

per lot are Poisson distributed.

a) 0.9463 b) 0.0537 c) 0.1128 d) 0.2417 e) 0.3452

A medical researcher estimates that .00004 of the population
has a rare blood

disorder. If the researcher randomly selects 100,000 people
from the population,

Answer questions 26-27 based on the above information using
Poisson

Approximation to Binomial problems.

26. What is the probability that seven or more people will
have the rare blood

disorder?

a) 0.0298 b) 0.0511 c) 0.8894 d) 0.0595 e) 0.1106

27. What is the probability that more than 10 people will
have the rare blood

disorder?

a) 0.0081 b) 0.9972 c) 0.0019 d) 0.0028 e) 0.9919

A high percentage of people who fracture or dislocate a bone
see a doctor for that

condition. Suppose the percentage is 99%. Consider a sample
in which 300 people

are randomly selected who have fractured or dislocated a
bone.

Answer questions 28-30 based on the above information using
Poisson

Approximation to Binomial problems.

28. What is the expected number of people who would not see a
doctor?

a) 297 b) 3 c) 30 d) 300 e) 1

29. What is the probability that exactly five of them did not
see a doctor?

a) 0.0504 b) 0.9161 c) 0.1008 d) 0.1680 e) 0.8992

30. What is the probability that fewer than four of them did
not see a doctor?

a) 0.1680 b) 0.8153 c) 0.1008 d) 0.2528 e) 0.6472

31. Assume that a random variable has a Poisson distribution
with a mean of 5

occurrences per ten minutes. The number of occurrences per
hour follows a Poisson

distribution with λ equal to _________

a) 5 b) 60 c) 30 d) 10 e) 20

32. The Poisson distribution is being used to approximate a
binomial distribution. If

n=40 and p=0.06, what value of lambda would be used?

a) 0.06 b) 2.4 c) 0.24 d) 24 e) 40

33. The number of phone calls arriving at a switchboard in a
10 minute time period

would best be modeled with the _________.

a) binomial distribution

b) hypergeometric distribution c) Poisson distribution

d) hyperbinomial distribution e) exponential distribution

34. The number of defects per 1,000 feet of extruded plastic
pipe is best modeled

with the ________________.

a) Poisson distribution

b) Pascal distribution

c) binomial distribution

d) hypergeometric distribution e) exponential distribution

35. The hypergeometric distribution must be used instead of
the binomial

distribution when ______

a) sampling is done with replacement

b) sampling is done without replacement c) n≥5% N

d) both b and c

e) there are more than two possible outcomes

36. The probability of selecting 3 defective items and 7 good
items from a warehouse

containing 10 defective and 50 good items would best be
modeled with the _______.

a) binomial distribution

b) hypergeometric distribution c) Poisson distribution

d) hyperbinomial distribution e) exponential distribution

Circuit boards for wireless telephones are etched, in an acid
bath, in batches of 100

boards. A sample of seven boards is randomly selected from
each lot for inspection.

A batch contains two defective boards; and x is the number of
defective boards in the

sample.

Answer questions 37-39 based on the above information.

37. P(x=1) is _______.

a) 0.1315 b) 0.8642 c) 0.0042 d) 0.6134 e) 0.6789

38. P(x=2) is _______.

a) 0.1315 b) 0.8642 c) 0.0042 d) 0.6134 e) 0.0034

39. P(x=0) is _______.

a) 0.1315 b) 0.8642 c) 0.0042 d) 0.6134 e) 0.8134

40. A large industrial firm allows a discount on any invoice
that is paid within 30

days. Of all invoices, 10% receive the discount.

In a company audit, 10 invoices are sampled at random. The
probability that fewer

than 3 of the 10 sampled invoices receive the discount is
approximately __________.

a) 0.1937 b) 0.057 c) 0.001 d) 0.3486 e) 0.9298

41. In a certain communications system, there is an average
of 1 transmission error

per 10 seconds. Assume that the distribution of transmission
errors is Poisson. The

probability of 1 error in a period of one-half minute is
approximately ________.

a) 0.1493 b) 0.3333 c) 0.3678 d) 0.1336 e) 0.03

42. It is known that screws produced by a certain company
will be defective with

probability .01 independently of each other. The company
sells the screws in

packages of 25 and offers a money-back guarantee that at most
1 of the 25 screws is

defective. Using Poisson approximation for binomial
distribution, the probability

that the company must replace a package is approximately
_________

a) 0.01 b) 0.1947 c) 0.7788 d) 0.0264 e) 0.2211

On Monday mornings, the First National Bank only has one
teller window open for

deposits and withdrawals. Experience has shown that the
average number of

arriving customers in a four-minute interval on Monday
mornings is 2.8, and each

teller can serve more than that number efficiently. These
random arrivals at this

bank on Monday mornings are Poisson distributed.

Answer the questions 43-50 based on the above information.

43. What is the probability that on a Monday morning exactly
six customers will

arrive in a four-minute interval?

a) 0.9756 b) 0.0872 c) 0.9593 d) 0.0163 e) 0.0407

44. What is the probability that no one will arrive at the
bank to make a deposit or

withdrawal during a four-minute interval?

a) 0.9392 b) 0.1703 c) 0.0608 d) 0.0000 e) 0.8297

45. Suppose the teller can serve no more than four customers
in any four-minute

interval at this window on a Monday morning. What is the
probability that, during

any given four-minute interval, the teller will be unable to
meet the demand?

a) 0.8477 b) 0.1523 c) 0.1557 d) 0.8443 e) 0.3081

46. Suppose the teller can serve no more than four customers
in any four-minute

interval at this window on a Monday morning. What is the
probability that the teller

will be able to meet the demand?

a) 0.8477 b) 0.1557 c) 0.8443 d) 0.1523 e) 0.3081

47. When demand cannot be met during any given interval, a
second window is

opened. What percentage of the time will a second window have
to be opened?

a) 0.8477 b) 0.8443 c) 0.1557 d) 0.1523 e) 0.3081

48. What is the probability that exactly three people will
arrive at the bank during a

two- minute period on Monday mornings to make a deposit or a
withdrawal?

a) 0.1082 b) 0.0026 c) 0.2225 d) 0.1128 e) 0.0407

49. What is the probability that five or more customers will
arrive during an eight

minute period?

a) 0.1523 b) 0.0143 c) 0.6579 d) 0.3421 e) 0.8477

50. On Saturdays, cars arrive at Sami Schmitt's Scrub and
Shine Car Wash at the rate

of 6 cars per fifteen minute interval. Using the Poisson
distribution, the probability

that five cars will arrive during the next five minute
interval is _____________.

a) 0.1008 b) 0.0361 c) 0.1339 d) 0.1606 e) 0.3610

Chp. 6: Questions 51-100.

51. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12), then

the height of this distribution, f(x), is ...

a) 1/8 b) 1/4 c) 1/12 d) 1/20 e) 1/24

52. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then the mean of this distribution is _____.

a) 10

b) 20

c) 5

d) 0

e) unknown

53. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then the standard deviation of this distribution is
__________________.

a) 4.00 b) 1.33 c) 1.15 d) 2.00 e) 1.00

54. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then the probability, P(9 x 11), is ____.

a) 0.250 b) 0.500 c) 0.333 d) 0.750 e) 1.000

55. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then the probability, P(10.0 x 11.5), is _.

a) 0.250 b) 0.333 c) 0.375 d) 0.500 e) 0.750

56. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then the probability, P(13 x 15), is __________________.

a) 0.250 b) 0.500 c) 0.375 d) 0.000 e) 1.000

57. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then P(x < 7) is __________________.

a) 0.500 b) 0.000 c) 0.375 d) 0.250 e) 1.000

58. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then P(x 11) is ________.

a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 1.000

59. If x is uniformly distributed over the interval 8 to 12,
inclusively (8 x 12),

then P(x 10) is __________________.

a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 0.900

60. If a continuous random variable x is uniformly
distributed over the interval 8 to

12, inclusively, then P(x = exactly 10) is __.

a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 0.900

61. The normal distribution is an example of

a) a discrete distribution

b) a continuous distribution c) a bimodal distribution

d) an exponential distribution e) a binomial distribution

62. The total area underneath any normal curve is equal to
_______.

a) the mean

b) one

c) the variance

d) the coefficient of variation e) the standard deviation

63. The area to the left of the mean in any normal
distribution is equal to _______.

a) the mean

b) 1

c) the variance d) 0.5

e) -0.5

64. A standard normal distribution has the following
characteristics:

a) the mean and the variance are both equal to 1

b) the mean and the variance are both equal to 0

c) the mean is equal to the variance

d) the mean is equal to 0 and the variance is equal to 1

e) the mean is equal to the standard deviation

65. If x is a normal random variable with mean 80 and
standard deviation 5, the zscore for x = 88 is ________.

a) 1.8 b) -1.8 c) 1.6 d) -1.6 e) 8.0

66. Suppose x is a normal random variable with mean 60 and
standard deviation 2.

A z score was calculated for a number, and the z score is
3.4. What is x?

a) 63.4

b) 56.6 c) 68.6 d) 53.2 e) 66.8

67. Suppose x is a normal random variable with mean 60 and
standard deviation 2.

A z score was calculated for a number, and the z score is
-1.3. What is x?

a) 58.7 b) 61.3 c) 62.6 d) 57.4 e) 54.7

68. Let z be a normal random variable with mean 0 and
standard deviation 1. What

is P(z < 1.3)?

a) 0.4032 b) 0.9032 c) 0.0968 d) 0.3485 e) 0. 5485

69. Let z be a normal random variable with mean 0 and
standard deviation 1. What

is P(1.3 < z < 2.3)?

a) 0.4032 b) 0.9032 c) 0.4893 d) 0.0861 e) 0.0086

70. Let z be a normal random variable with mean 0 and
standard deviation 1. What

is P(z > 2.4)?

a) 0.4918 b) 0.9918 c) 0.0082 d) 0.4793 e) 0.0820

71. Let z be mean 0 and P(z < -2.1)?

a) 0.4821 b) -0.4821 c) 0.9821 d) 0.0179 e) -0.0179

72.Let z be a normal random variable with

mean 0 standard deviation 1. What isP(z > -1.1)?

a) 0.36432 b) 0.8643 c) 0.1357 d) -0.1357 e) -0.8643

73.Let z be a normal random variable with

mean 0 and standard deviation 1. What is P(-2.25 < z
< -1.1)?

a) 0.36432 b) 0.8643 c) 0.1357 d) -0.1357 e) -0.8643

74. The expected (mean) life of a particular type of light
bulb is 1,000 hours with a standard deviation of

50 hours. The life of this bulb is normally distributed. What
is the probability that a randomly selected bulb

would last longer than 1150 hours?

a) 0.4987 b) 0.9987 c) 0.0013 d) 0.5013 e) 0.5513

75. The expected (mean) life of a particular type of light
bulb is 1,000 hours with a

standard deviation of 50 hours. The life of

a) 0.3643 b) 0.8643 c) 0.1235 d) 0.4878 e) 0.5000

76. The expected (mean) life of a particular type of light
bulb is 1,000 hours with a

standard deviation of 50 hours. The life of this bulb is
normally distributed. What is

the probability that a randomly selected bulb would last
fewer than 940 hours?

a) 0.3849 b) 0.8849 c) 0.1151 d) 0.6151 e) 0.6563

77. Suppose you are working with a data set that is normally
distributed with a

mean of 400 and a standard deviation of 20. Determine the
value of x such that 60%

of the values are greater than x.

a) 404.5 b) 395.5 c) 405.0 d) 395.0 e) 415.0

According to a report by Scarborough Research, the average
monthly household

cellular phone bill is $60. Suppose local monthly household
cell phone bills are

normally distributed with a standard deviation of $11.35.

Answer questions 78-81 based on the above information.

78. What is the probability that a randomly selected monthly
cell phone bill is more

than $85?

a) 0.4861 b) 0.9861 c) 0.6139 d) 0.5000 e) 0.0139

79. What is the probability that a randomly selected monthly
cell phone bill is

between $45 and $70?

a) 0.8106 b) 0.9066 c) 0.7172 d) 0.4066 e) 0.3106

80. What is the probability that a randomly selected monthly
cell phone bill is

between $65 and $75?

a) 0.2366 b) 0.1700 c) 0.4066 d) 0.0934 e) 0.6700

81. What is the probability that a randomly selected monthly
cell phone bill is no

more than $40?

a) 0.4987 b) 0.4608 c) 0.5000 d) 0.9608 e) 0.0392

82. According to Student Monitor, a New Jersey research firm,
the average cumulated

college student loan debt for a graduating senior is
$25,760.Assume that the

standard deviation of such student loan debt is

$5,684. Thirty percent of these graduating seniors owe more
than what amount?

a) $28,715.68 b) $2,955.68 c) $22,804.32 d) $28,809.28 e)
$28,359.68

83. Let x be a binomial random variable with n=20 and p=.8.
If we use the normal

distribution to approximate probabilities for this, we would
use a mean of _______.

a) 20 b) 16 c) 3.2 d) 8 e) 5

84. Let x be a binomial random variable with n=100 and p=.8.
If we use the normal

distribution to approximate probabilities for this, a
correction for continuity should

be made. To find the probability of more than 12 successes,
we should find _______.

a) P(x>12.5) b) P(x>12) c) P(x>11.5) d)
P(x<11.5) e) P(x < 12)

A study about strategies for competing in the global
marketplace states that 52% of

the respondents agreed that companies need to make direct
investments in foreign

countries. It also states that about 70% of those responding
agree that it is attractive

to have a joint venture to increase global competitiveness.
Suppose CEOs of 95

manufacturing companies are randomly contacted about global
strategies.

Using Normal Approximation of Binomial Distribution with
correction for

continuity, answer questions 85-88 based on above
information.

85. What is the probability that between 44 and 52
(inclusive) CEOs agree that

companies should make direct investments in foreign
countries?

a) 0.3869 b) 0.2389 c) 0.6258 d) 0.5013 e) 0.7389

86. What is the probability that more than 56 CEOs agree with
that assertion?

a) 0.4279 b) 0.8279 c) 0.5000 d) 0.0721 e) 0.5721

87. What is the probability that fewer than 60 CEOs agree
that it is attractive to have

a joint venture to increase global competitiveness?

a) 0.5000 b) 0.0582 c) 0.4418 d) 0.9418 e) 0.5582

88. What is the probability that between 55 and 62
(inclusive) CEOs agree with that

assertion?

a) 0.4963 b) 0.9963 c) 0.3133 d) 0.8099

e) 0.1830

89. The average length of time between arrivals at a turnpike
tollbooth is 23

seconds. Assume that the time between arrivals at the
tollbooth is exponentially

distributed. What is the probability that a minute or more
will elapse between

arrivals?

a) 0.9265 b) 0.0435 c) 0.4365 d) 0.0735 e) 0.5000

90. The average length of time between arrivals at a turnpike
tollbooth is 23

seconds. Assume that the time between arrivals at the
tollbooth is exponentially

distributed. If a car has just passed through the tollbooth,
what is the probability

that no car will show up for at least 3 minutes?

a) 0.0004 b) 0.9996 c) 0.4996 d) 0.0435 e) 0.9265

During the summer at a small private airport in western
Nebraska, the unscheduled

arrival of airplanes is Poisson distributed with an average
arrival rate of 1.12 planes

per hour.

Answer questions 91-93 based on the above information.

91. What is the average interarrival time between planes (in
minutes)?

a) 53.6 b) 67.2 c) 53.4 d) 60

e) 58.88

92. What is the probability that at least 2 hours will elapse
between plane arrivals?

a) 0.5000 b) 0.8935 c) 0.3935 d) 0.6065 e) 0.1065

93. What is the probability of two planes arriving less than
10 minutes apart?

a) 0.8297 b) 0.1703 c) 0.6703 d) 0.3297 e) 0.5000

94. The probability that a call to an emergency help line is
answered in less than 10

seconds is 0.8. Assume that the calls are independent of each
other. Using the normal

approximation for binomial with a correction for continuity,
the probability that at

least 75 of 100 calls are answered within 10 seconds is
approximately _______

a) 0.8

b) 0.1313 c) 0.5235 d) 0.9154 e) 0.8687

95. Inquiries arrive at a record message device according to
a Poisson process of rate

15 inquiries per minute. The probability that it takes more
than 12 seconds for the

first inquiry to arrive is approximately _________

a) 0.05

b) 0.75

c) 0.25

d) 0.27

e) 0.73

96. On Saturdays, cars arrive at Sam Schmitt's Scrub and
Shine Car Wash at the rate

of 6 cars per fifteen minute interval. The probability that
at least 2 minutes will

elapse between car arrivals is _____________.

a) 0.0000 b) 0.4493 c) 0.1353 d) 1.0000 e) 1.0225

97. On Saturdays, cars arrive at Sam Schmitt's Scrub and
Shine Car Wash at the rate

of 6 cars per fifteen minute interval. The probability that
less than 10 minutes will

elapse between car arrivals is _________.

a) 0.8465 b) 0.9817 c) 0.0183 d) 0.1535 e) 0.2125

98. Incoming phone calls generally are thought to be Poisson
distributed. If an

operator averages 2.2 phone calls every 30 seconds, what is
the expected (average)

amount of time between calls (in seconds)?

a) 66

b) 30

c) 13.64 d) 60

e) 27.27

99. Incoming phone calls generally are thought to be Poisson
distributed. If an

operator averages 2.2 phone calls every 30 seconds, what is
the probability that a

minute or more would elapse between incoming calls?

a) 0.9877 b) 0.5123

c) 0.4877 d) 0.5000 e) 0.0123

100. Incoming phone calls generally are thought to be Poisson
distributed. If an

operator averages 2.2 phone calls every 30 seconds, what is
the probability that at

least two minutes would elapse between incoming calls?

a) 0.0002 b) 0.9998 c) 0.4998 d) 0.5000 e) 0.5002

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