Continuous Random Variable MCQs with Solution - 2
51. In a popular shopping centre, the
waiting time for an ABSA ATM machine is found to be uniformly distributed
between 1 and 5 minutes. What is the
expected waiting time (in minutes) for the ATM to be free to use?
a. 2 minutes
b. 5 minutes
*c. 3 minute
d. 4 minutes
e. 0.25 minutes
52. In a popular shopping centre, the
waiting time for an ABSA ATM machine is found to be uniformly distributed
between 1 and 9 minutes. What is the
expected waiting time (in minutes) for the ATM to be free to use?
a. 2 minutes
*b. 5 minutes
c. 3 minute
d. 4 minutes
e. 0.25 minutes
53. In a popular shopping centre, the
waiting time for an ABSA ATM machine is found to be uniformly distributed
between 1 and 7 minutes. What is the
expected waiting time (in minutes) for the ATM to be free to use?
a. 2 minutes
b. 5 minutes
c. 3 minute
*d. 4 minutes
e. 0.25 minutes
54. If the continuous random variable X is
uniformly distributed over the interval [15,20] then the mean of X is:
*a. 17.5
b. 15
c. 25
d. 35
e. none of the above
55. If X ~ U(12, 18), what is the standard
deviation of X?
*a. 1.73
b. 1.15
c. 1.44
d. 2.02
e. 0.87
56. If X ~ U(15, 19), what is the standard
deviation of X?
a. 1.73
*b. 1.15
c. 1.44
d. 2.02
e. 0.87
57. If X ~ U(11, 16), what is the standard
deviation of X?
a. 1.73
b. 1.15
*c. 1.44
d. 2.02
e. 0.87
58. If X ~ U(13, 20), what is the standard
deviation of X?
a. 1.73
b. 1.15
c. 1.44
*d. 2.02
e. 0.87
59. If X ~ U(14, 17), what is the standard
deviation of X?
a. 1.73
b. 1.15
c. 1.44
d. 2.02
*e. 0.87
60. If X ~ U(12, 18), what is the variance
of X?
*a. 3.00
b. 1.33
c. 2.08
d. 4.08
e. 0.75
61. If X ~ U(15, 19), what is the variance
of X?
a. 3.00
*b. 1.33
c. 2.08
d. 4.08
e. 0.75
62. If X ~ U(11, 16), what is the variance
of X?
a. 3.00
b. 1.33
*c. 2.08
d. 4.08
e. 0.75
63. If X ~ U(13, 20), what is the variance
of X?
a. 3.00
b. 1.33
c. 2.08
*d. 4.08
e. 0.75
64. If X ~ U(14, 17), what is the variance
of X?
a. 3.00
b. 1.33
c. 2.08
d. 4.08
*e. 0.75
65. The length of time it takes to wait in
the queue on registration day at a certain university is uniformly distributed
between 10 minutes and 2 hours. What is
the variance of the waiting time?
*a. 1008 minutes2
b. 31.8 minutes
c. 65 minutes2
d. 100 minutes2
e. 25 minutes
66. The length of time it takes to wait in
the queue on registration day at a certain university is uniformly distributed
between 10 minutes and 2 hours. What is
the standard deviation of the waiting time?
a. 1008 minutes2
*b. 31.8 minutes
c. 65 minutes2
d. 100 minutes2
e. 25 minutes
67. The mass of a 1000g
container of yoghurt is equally likely to take on any value in the interval
(995g,1010g). The container will not contain less than 995g or more than 1010g
of yoghurt. What is the expected mass of
the yoghurt container?
a. 1000g
*b. 1002.5g
c. 1010g
d. 995g
e. 1005g
68. The mass of a 1000g
container of yoghurt is equally likely to take on any value in the interval
(995g,1010g). The container will not contain less than 995g or more than 1010g
of yoghurt. What is the standard
deviation of the mass of the yoghurt container?
a. 18.75g
b. 21.46g
c. 2.15g
*d. 4.33g
e. 3.43g
69. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. A student arrives at university 10 minutes before the scheduled
start of her first lecture. What is the probability that it will take the
student more than 10 minutes to find a parking space, causing her to be late
for her lecture?
*a. 0.082
b. 0.024
c. 0.287
d. 0.135
e. 0.368
70. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. A student arrives at university 15 minutes before the scheduled
start of her first lecture. What is the probability that it will take the
student more than 15 minutes to find a parking space, causing her to be late
for her lecture?
a. 0.082
*b. 0.024
c. 0.287
d. 0.135
e. 0.368
71. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. A student arrives at university 5 minutes before the scheduled start
of her first lecture. What is the probability that it will take the student
more than 5 minutes to find a parking space, causing her to be late for her
lecture?
a. 0.082
b. 0.024
*c. 0.287
d. 0.135
e. 0.368
72. Let X represent the amount of time it takes
a student to find a parking space in the parking lot at a university. We know that the distribution of X can be
modelled using an exponential distribution with a mean of 5 minutes. A student
arrives at university 10 minutes before the scheduled start of her first
lecture. What is the probability that it will take the student more than 10
minutes to find a parking space, causing her to be late for her lecture?
a. 0.082
b. 0.024
c. 0.287
*d. 0.135
e. 0.368
73. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 5 minutes. A student arrives at university 5 minutes before the scheduled
start of her first lecture. What is the probability that it will take the
student more than 5 minutes to find a parking space, causing her to be late for
her lecture?
a. 0.082
b. 0.024
c. 0.287
d. 0.135
*e. 0.368
74. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. What is the probability that it takes a randomly selected student
between 2 and 12 minutes to find a parking space in the parking lot?
*a. 0.557
b. 0.524
c. 0.471
d. 0.233
e. 0.204
75. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. What is the probability that it takes a randomly selected student
between 2 and 10 minutes to find a parking space in the parking lot?
a. 0.557
*b. 0.524
c. 0.471
d. 0.233
e. 0.204
76. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. What is the probability that it takes a randomly selected student
between 2 and 8 minutes to find a parking space in the parking lot?
a. 0.557
b. 0.524
*c. 0.471
d. 0.233
e. 0.204
77. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. What is the probability that it takes a randomly selected student
between 4 and 8 minutes to find a parking space in the parking lot?
a. 0.557
b. 0.524
c. 0.471
*d. 0.233
e. 0.204
78. Let X represent the amount of time it
takes a student to find a parking space in the parking lot at a
university. We know that the
distribution of X can be modelled using an exponential distribution with a mean
of 4 minutes. What is the probability that it takes a randomly selected student
between 5 and 10 minutes to find a parking space in the parking lot?
a. 0.557
b. 0.524
c. 0.471
d. 0.233
*e. 0.204
79. A small bank branch has a single teller to handle
transactions with customers. Customers arrive at the bank at an average rate of
one every three minutes. What is the
probability that it will be more than 10 minutes before the first customer
arrives for the day after the bank has opened at 8am ?
*a. 0.036
b. 0.189
c. 0.368
d. 0.097
e. 0.018
80. A small bank branch has a single teller to handle
transactions with customers. Customers arrive at the bank at an average rate of
one every three minutes. What is the
probability that it will be more than 5 minutes before the first customer
arrives for the day after the bank has opened at 8am ?
a. 0.036
*b. 0.189
c. 0.368
d. 0.097
e. 0.018
81. A small bank branch has a single teller to handle
transactions with customers. Customers arrive at the bank at an average rate of
one every three minutes. What is the
probability that it will be more than 3 minutes before the first customer
arrives for the day after the bank has opened at 8am ?
a. 0.036
b. 0.189
*c. 0.368
d. 0.097
e. 0.018
82. A small bank branch has a single teller to handle
transactions with customers. Customers arrive at the bank at an average rate of
one every three minutes. What is the
probability that it will be more than 7 minutes before the first customer
arrives for the day after the bank has opened at 8am ?
a. 0.036
b. 0.189
c. 0.368
*d. 0.097
e. 0.018
83. A small bank branch has a single teller to handle
transactions with customers. Customers arrive at the bank at an average rate of
one every three minutes. What is the
probability that it will be more than 12 minutes before the first customer
arrives for the day after the bank has opened at 8am ?
a. 0.036
b. 0.189
c. 0.368
d. 0.097
*e. 0.018
84. The time it takes a technician to fix a
computer is exponentially distributed with a mean of 15 minutes. What is the probability that it will take the
technician less than 10 minutes to fix a randomly selected computer?
*a. 0.487
b. 0.373
c. 0.632
d. 0.393
e. 0.551
85. The time it takes a technician to fix a
computer is exponentially distributed with a mean of 15 minutes. What is the probability that it will take the
technician less than 7 minutes to fix a randomly selected computer?
a. 0.487
*b. 0.373
c. 0.632
d. 0.393
e. 0.551
86. The time it takes a technician to fix a
computer is exponentially distributed with a mean of 15 minutes. What is the probability that it will take the
technician less than 15 minutes to fix a randomly selected computer?
a. 0.487
b. 0.373
*c. 0.632
d. 0.393
e. 0.551
87. The time it takes a technician to fix a
computer is exponentially distributed with a mean of 10 minutes. What is the probability that it will take the
technician less than 5 minutes to fix a randomly selected computer?
a. 0.487
b. 0.373
c. 0.632
*d. 0.393
e. 0.551
88. The time it takes a technician to fix a
computer is exponentially distributed with a mean of 10 minutes. What is the probability that it will take the
technician less than 8 minutes to fix a randomly selected computer?
a. 0.487
b. 0.373
c. 0.632
d. 0.393
*e. 0.551
89. Flaws occur in telephone cabling at an
average rate of 4.4 flaws per 1km of cable.
What is the probability that the distance between two flaws exceeds
0.5km?
*a. 0.111
b. 0.012
c. 0.001
d. 0.202
e. 0.041
90. Flaws occur in telephone cabling at an
average rate of 4.4 flaws per 1km of cable.
What is the probability that the distance between two flaws exceeds 1km?
a. 0.111
*b. 0.012
c. 0.001
d. 0.202
e. 0.041
91. Flaws occur in telephone cabling at an
average rate of 4.4 flaws per 1km of cable.
What is the probability that the distance between two flaws exceeds
1.5km?
a. 0.111
b. 0.012
*c. 0.001
d. 0.202
e. 0.041
92. Flaws occur in telephone cabling at an
average rate of 3.2 flaws per 1km of cable.
What is the probability that the distance between two flaws exceeds 0.5km?
a. 0.111
b. 0.012
c. 0.001
*d. 0.202
e. 0.041
93. Flaws occur in telephone cabling at an
average rate of 3.2 flaws per 1km of cable.
What is the probability that the distance between two flaws exceeds 1km?
a. 0.111
b. 0.012
c. 0.001
d. 0.202
*e. 0.041
94. Textbooks are sold at a university
bookshop at an average rate of 2 per hour.
What is the probability that it will be less than 20 minutes before the
next textbook is sold?
*a. 0.487
b. 0.283
c. 0.632
d. 0.528
e. 0.393
95. Textbooks are sold at a university
bookshop at an average rate of 2 per hour.
What is the probability that it will be less than 10 minutes before the
next textbook is sold?
a. 0.487
*b. 0.283
c. 0.632
d. 0.528
e. 0.393
96. Textbooks are sold at a university
bookshop at an average rate of 2 per hour.
What is the probability that it will be less than 30 minutes before the
next textbook is sold?
a. 0.487
b. 0.283
*c. 0.632
d. 0.528
e. 0.393
97. Textbooks are sold at a university
bookshop at an average rate of 3 per hour.
What is the probability that it will be less than 15 minutes before the
next textbook is sold?
a. 0.487
b. 0.283
c. 0.632
*d. 0.528
e. 0.393
98. Textbooks are sold at a university
bookshop at an average rate of 3 per hour.
What is the probability that it will be less than 10 minutes before the
next textbook is sold?
a. 0.487
b. 0.283
c. 0.632
d. 0.528
*e. 0.393
99. The time it takes a technician to fix a
computer is exponentially distributed with a mean of 15 minutes. What is the variance of the amount of time it
takes a technician to fix a computer?
*a. 225
b. 15
c. 0.004
d. 0.067
e. 20
100. The time it takes a technician to fix
a computer is exponentially distributed with a mean of 15 minutes. What is the standard deviation of the amount
of time it takes a technician to fix a computer?
a. 225
*b. 15
c. 0.004
d. 0.067
e. 20
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