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 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) n5% 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 z- score 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.
Letz
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 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. xP(x) 00.1010.1020.5030.303. 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 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) n5% 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 z- score 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.
Letz
be
mean 0 and P(z
< -2.1)?a) 0.4821 b) -0.4821 c) 0.9821 d) 0.0179 e) -0.017972.Let z be a normal random variable 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) -0.864374. 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