Continuous Random Variable MCQs with Solution - 3
Note: Correct Option is Marked (*)
101. The time it takes a technician to fix
a computer is exponentially distributed with a mean of 10 minutes. What is the variance of the amount of time it
takes a technician to fix a computer?
a. 0.01
b. 0.1
*c. 100
d. 10
e. 20
102. The time it takes a technician to fix
a computer is exponentially distributed with a mean of 10 minutes. What is the standard deviation of the amount
of time it takes a technician to fix a computer?
a. 0.01
b. 0.1
c. 100
*d. 10
e. 20
103. The time it takes a technician to fix
a computer is exponentially distributed with a mean of 20 minutes. What is the standard deviation of the amount
of time it takes a technician to fix a computer?
a. 0.05
b. 15
c. 100
d. 10
*e. 20
104. Flaws occur in telephone cabling at an
average rate of 4.4 flaws per 1km of cable.
What is the expected distance between flaws (in km)?
a. 4.4
b. 3.2
*c. 0.227
d. 0.313
e. 2.2
105. Flaws occur in telephone cabling at an
average rate of 3.2 flaws per 1km of cable.
What is the expected distance between flaws (in km)?
a. 4.4
b. 3.2
c. 0.227
*d. 0.313
e. 2.2
106. Flaws occur in telephone cabling at an
average rate of 4.4 flaws per 1km of cable.
What is the variance of the distance between flaws?
*a. 0.052
b. 0.098
c. 19.36
d. 10.24
e. 2.2
107. Flaws occur in telephone cabling at an
average rate of 3.2 flaws per 1km of cable.
What is the variance of the distance between flaws?
a. 0.052
*b. 0.098
c. 19.36
d. 10.24
e. 2.2
108. Cars arrive at a tollgate at an
average rate of 10 cars per hour. What
is the mean time between arrivals (in minutes)?
*a. 6 minutes
b. 0.1 minutes
c. 3 minutes
d. 0.05 minutes
e. 4 minutes
109. Cars arrive at a tollgate at an
average rate of 20 cars per hour. What
is the mean time between arrivals (in minutes)?
a. 6 minutes
b. 0.1 minutes
*c. 3 minutes
d. 0.05 minutes
e. 4 minutes
110. Cars arrive at a tollgate at an
average rate of 15 cars per hour. What
is the mean time between arrivals (in minutes)?
a. 6 minutes
b. 0.1 minutes
c. 3 minutes
d. 0.05 minutes
*e. 4 minutes
111. The convenor of a first-year
statistics programme at a certain university receives, on average, 5 emails per
30 minutes. What is the mean time
between the arrival of emails in her inbox (in minutes)?
a. 30 minutes
b. 0.167 minutes
*c. 6 minutes
d. 0.5 minutes
e. 5 minutes
112. The convenor of a first-year
statistics programme at a certain university receives, on average, 5 emails per
30 minutes. What is the variance of the
time between the arrival of emails in her inbox?
a. 36 minutes
*b. 36 minutes2
c. 6 minutes
d. 6 minutes2
e. 0.028 minutes2
113. Calls are received by the switchboard
of a large company at an average rate of 10 calls every 15 minutes. What is the mean time between calls (in
minutes)?
a. 2 minutes
b. 0.67 minutes
c. 15 minutes
d. 10 minutes
*e. 1.5 minutes
114. You and I own a company called
Deliveries Inc. We have a large fleet of delivery trucks. On average we have 10
breakdowns per 5 day working week. What is the expected time (in days) between
breakdowns?
a. 1 day
*b. 0.5 day
c. 2 days
d. 0.75 day
e. 5 days
115. You own a very old car which breaks
down, on average, 3 times a year. What
is the mean time between break downs, in months, of your car?
a. 3 months
b. 0.25 months
c. 12 months
*d. 4 months
e. 0.5 months
116. You own a very old car which breaks
down, on average, 3 times a year. What
is the standard deviation of the time between break downs, in months, of your
car?
a. 3 months
b. 0.25 months
c. 12 months
*d. 4 months
e. 0.5 months
117. The diameters of oranges found in the
orchard of an orange farm follow a normal distribution with a mean of 120mm and
a standard deviation of 10mm. What
proportion of oranges in the orchard have a diameter between 110mm and 130mm?
*a. 0.6826
b. 0.8186
c. 0.3829
d. 0.4332
e. 0.2858
118. The diameters of oranges found in the
orchard of an orange farm follow a normal distribution with a mean of 120mm and
a standard deviation of 10mm. What
proportion of oranges in the orchard have a diameter between 110mm and 140mm?
a. 0.6826
*b. 0.8186
c. 0.3829
d. 0.4332
e. 0.2858
119. The diameters of oranges found in the
orchard of an orange farm follow a normal distribution with a mean of 120mm and
a standard deviation of 10mm. What proportion
of oranges in the orchard have a diameter between 115mm and 125mm?
a. 0.6826
b. 0.8186
*c. 0.3829
d. 0.4332
e. 0.2858
120. The diameters of oranges found in the
orchard of an orange farm follow a normal distribution with a mean of 120mm and
a standard deviation of 10mm. What
proportion of oranges in the orchard have a diameter between 105mm and 120mm?
a. 0.6826
b. 0.8186
c. 0.3829
*d. 0.4332
e. 0.2858
121. The diameters of oranges found in the
orchard of an orange farm follow a normal distribution with a mean of 120mm and
a standard deviation of 10mm. What
proportion of oranges in the orchard have a diameter between 100mm and 115mm?
a. 0.6826
b. 0.8186
c. 0.3829
d. 0.4332
*e. 0.2858
122. The random variable X is normally
distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is within one
standard deviation of the mean?
*a. 0.683
b. 0.954
c. 0.271
d. 0.340
e. 0.161
123. The random variable X is normally
distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 50
and 90?
a. 0.683
*b. 0.954
c. 0.271
d. 0.340
e. 0.161
124. The random variable X is normally
distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 65
and 72?
a. 0.683
b. 0.954
*c. 0.271
d. 0.340
e. 0.161
125. The random variable X is normally
distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72
and 84?
a. 0.683
b. 0.954
c. 0.271
*d. 0.340
e. 0.161
126. The random variable X is normally
distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 50
and 61?
a. 0.683
b. 0.954
c. 0.271
d. 0.340
*e. 0.161
127. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
*a. 0.819
b. 0.242
c. 0.286
d. 0.533
e. 0.307
128. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. 0.819
*b. 0.242
c. 0.286
d. 0.533
e. 0.307
129. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. 0.819
b. 0.242
*c. 0.286
d. 0.533
e. 0.307
130. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. 0.819
b. 0.242
c. 0.286
*d. 0.533
e. 0.307
131. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. 0.819
b. 0.242
c. 0.286
d. 0.533
*e. 0.307
132. Given that X is Normally distributed
with a mean of 80 and a variance of 100, what is p(85 < X < 90)?
*a. 0.150
b. 0.341
c. 0.286
d. 0.625
e. 0.533
133. Given that X is Normally distributed
with a mean of 80 and a variance of 100, what is p(70 < X < 80)?
a. 0.150
*b. 0.341
c. 0.286
d. 0.625
e. 0.533
134. Given that X is Normally distributed
with a mean of 80 and a variance of 100, what is p(60 < X < 75)?
a. 0.150
b. 0.341
*c. 0.286
d. 0.625
e. 0.533
135. Given that X is Normally distributed
with a mean of 80 and a variance of 100, what is p(75 < X < 95)?
a. 0.150
b. 0.341
c. 0.286
*d. 0.625
e. 0.533
136. Given that X is Normally distributed
with a mean of 80 and a variance of 100, what is p(70 < X < 85)?
a. 0.150
b. 0.341
c. 0.286
d. 0.625
*e. 0.533
137. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What proportion
of students are between 162cm and 182cm in height?
*a. 0.954
b. 0.601
c. 0.718
d. 0.883
e. 0.270
138. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What
proportion of students are between 170cm and 180cm in height?
a. 0.954
*b. 0.601
c. 0.718
d. 0.883
e. 0.270
139. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What
proportion of students are between 160cm and 175cm in height?
a. 0.954
b. 0.601
*c. 0.718
d. 0.883
e. 0.270
140. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What
proportion of students are between 165cm and 181cm in height?
a. 0.954
b. 0.601
c. 0.718
*d. 0.883
e. 0.270
141. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What
proportion of students are between 175cm and 185cm in height?
a. 0.954
b. 0.601
c. 0.718
d. 0.883
*e. 0.270
142. A statistical analysis of
long-distance telephone calls indicates that the length of these calls is
normally distributed with a mean of 240 seconds and a standard deviation of 40
seconds. What proportion of calls last
less than 180 seconds or more than 300 seconds?
a. 0.911
b. 0.034
*c. 0.134
d. 0.067
e. 0.548
143. A bakery finds that the average weight
of its most popular package of cookies is 32.06g with a standard deviation of
0.10g. Assuming that the weight of the
package of cookies follows a normal distribution, what portion of cookie
packages will weigh less than 31.90 g or more than 32.30 g?
*a. 0.06
b. 0.24
c. 0.78
d. 0.01
e. 0.00
144. A statistical analysis of
long-distance telephone calls indicates that the length of these calls is
normally distributed with a mean of 240 seconds and a standard deviation of 40
seconds. What proportion of calls lasts
less than 180 seconds?
a. 0.214
b. 0.094
c. 0933
d. 0.466
*e. 0.067
145. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What is
the probability that a randomly selected student from this class will be taller
than 180cm?
*a. 0.055
b. 0.655
c. 0.274
d. 0.919
e. 0.992
146. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What is
the probability that a randomly selected student from this class will be taller
than 170cm?
a. 0.055
*b. 0.655
c. 0.274
d. 0.919
e. 0.992
147. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What is
the probability that a randomly selected student from this class will be taller
than 175cm?
a. 0.055
b. 0.655
*c. 0.274
d. 0.919
e. 0.992
148. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a variance
of 25cm2. What is the
probability that a randomly selected student from this class will be taller
than 165cm?
a. 0.055
b. 0.655
c. 0.274
*d. 0.919
e. 0.992
149. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. What is
the probability that a randomly selected student from this class will be taller
than 160cm?
a. 0.055
b. 0.655
c. 0.274
d. 0.919
*e. 0.992
150. Using the standard normal table, the sum
of the probabilities to the right of z = 2.18 and to the left of z = -1.75 is:
a. 0.4854
b. 0.4599
c. 0.0146
d. 0.0401
*e. 0.0547
Comments
Post a Comment