Continuous Random Variable MCQs with Solution - 4
Note: Correct Option is Marked (*)
151. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours. What proportion of printers fails before
1000 hours?
*a. 0.0062
b. 0.0668
c. 0.8413
d. 0.0228
e. 0.6915
152. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours. What proportion of printers fails before
1200 hours?
a. 0.0062
*b. 0.0668
c. 0.8413
d. 0.0228
e. 0.6915
153. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours. What proportion of printers fails before
1700 hours?
a. 0.0062
b. 0.0668
*c. 0.8413
d. 0.0228
e. 0.6915
154. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours. What proportion of printers fails before
1100 hours?
a. 0.0062
b. 0.0668
c. 0.8413
*d. 0.0228
e. 0.6915
155. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours. What proportion of printers fails before
1600 hours?
a. 0.0062
b. 0.0668
c. 0.8413
d. 0.0228
*e. 0.6915
156. Student marks for a first-year
Statistics class test follow a normal distribution with a mean of 63% and a
standard deviation of 7%. What is the probability that a randomly selected
student who wrote the test got more than 75%?
*a. 0.043
b. 0.388
c. 0.159
d. 0.666
e. 0.968
157. Student marks for a first-year
Statistics class test follow a normal distribution with a mean of 63% and a standard
deviation of 7%. What is the probability that a randomly selected student who
wrote the test got more than 65%?
a. 0.043
*b. 0.388
c. 0.159
d. 0.666
e. 0.968
158. Student marks for a first-year
Statistics class test follow a normal distribution with a mean of 63% and a
standard deviation of 7%. What is the probability that a randomly selected
student who wrote the test got more than 70%?
a. 0.043
b. 0.388
*c. 0.159
d. 0.666
e. 0.968
159. Student marks for a first-year
Statistics class test follow a normal distribution with a mean of 63% and a
standard deviation of 7%. What is the probability that a randomly selected
student who wrote the test got more than 60%?
a. 0.043
b. 0.388
c. 0.159
*d. 0.666
e. 0.968
160. Student marks for a first-year Statistics
class test follow a normal distribution with a mean of 63% and a standard
deviation of 7%. What is the probability that a randomly selected student who
wrote the test got more than 50%?
a. 0.043
b. 0.388
c. 0.159
d. 0.666
*e. 0.968
161. The weights of newborn human babies
are normally distributed with a mean of 3.2kg and a standard deviation of
1.1kg. What is the probability that a
randomly selected newborn baby weighs less than 2.0kg?
*a. 0.138
b. 0.428
c. 0.766
d. 0.262
e. 0.607
162. The weights of newborn human babies
are normally distributed with a mean of 3.2kg and a standard deviation of
1.1kg. What is the probability that a
randomly selected newborn baby weighs less than 3.0kg?
a. 0.138
*b. 0.428
c. 0.766
d. 0.262
e. 0.607
163. The weights of newborn human babies
are normally distributed with a mean of 3.2kg and a standard deviation of
1.1kg. What is the probability that a
randomly selected newborn baby weighs less than 4.0kg?
a. 0.138
b. 0.428
*c. 0.766
d. 0.262
e. 0.607
164. The weights of newborn human babies
are normally distributed with a mean of 3.2kg and a standard deviation of
1.1kg. What is the probability that a
randomly selected newborn baby weighs less than 2.5kg?
a. 0.138
b. 0.428
c. 0.766
*d. 0.262
e. 0.607
165. The weights of newborn human babies
are normally distributed with a mean of 3.2kg and a standard deviation of
1.1kg. What is the probability that a
randomly selected newborn baby weighs less than 3.5kg?
a. 0.138
b. 0.428
c. 0.766
d. 0.262
*e. 0.607
166. Monthly expenditure on their credit
cards, by credit card holders from a certain bank, follows a normal
distribution with a mean of R1,295.00 and a standard deviation of R750.00. What proportion of credit card holders spend
more than R1,500.00 on their credit cards per month?
a. 0.487
*b. 0.392
c. 0.500
d. 0.791
e. 0.608
167. Let z be a standard normal value that
is unknown but identifiable by position and area. If the area to the right of z is 0.8413, then
the value of z must be:
a. 1.00
*b. -1.00
c. 0.00
d. 0.41
e. -0.41
168. Let z be a standard normal value that
is unknown but identifiable by position and area. If the symmetrical area between negative z
and positive z is 0.9544 then the value of z must be:
*a. 2.00
b. 0.11
c. 2.50
d. 0.06
e. 2.20
169. If the area to the right of a positive
value of z (z has a standard normal distribution) is 0.0869 then the value of z
must be:
a. 0.22
b. -1.36
*c. 1.36
d. 1.71
e. -1.71
170. If the area between 0 and a positive
value of z (z has a standard normal distribution) is 0.4591 then the value of z
is:
*a. 1.74
b. -1.74
c. 0.18
d. -0.18
e. 1.84
171. If the area to the left of a value of
z (z has a standard normal distribution) is 0.0793, what is the value of z?
*a. -1.41
b. 1.41
c. -2.25
d. 2.25
e. -0.03
172. If the area to the left of a value of
z (z has a standard normal distribution) is 0.0122, what is the value of z?
a. -1.41
b. 1.41
*c. -2.25
d. 2.25
e. -0.03
173. If the area to the left of a value of
z (z has a standard normal distribution) is 0.1867, what is the value of z?
*a. -0.89
b. 0.89
c. -1.02
d. 1.02
e. -2.37
174. If the area to the left of a value of
z (z has a standard normal distribution) is 0.1539, what is the value of z?
a. -0.89
b. 0.89
*c. -1.02
d. 1.02
e. -2.37
175. If the area to the left of a value of
z (z has a standard normal distribution) is 0.0089, what is the value of z?
a. -0.89
b. 0.89
c. -1.02
d. 1.02
*e. -2.37
176. If the area to the right of a value of
z (z has a standard normal distribution) is 0.0793, what is the value of z?
a. -1.41
*b. 1.41
c. -2.25
d. 2.25
e. -0.03
177. If the area to the right of a value of
z (z has a standard normal distribution) is 0.0122, what is the value of z?
a. -1.41
b. 1.41
c. -2.25
*d. 2.25
e. -0.03
178. If the area to the right of a value of
z (z has a standard normal distribution) is 0.1867, what is the value of z?
a. -0.89
*b. 0.89
c. -1.02
d. 1.02
e. -2.37
179. If the area to the right of a value of
z (z has a standard normal distribution) is 0.1539, what is the value of z?
a. -0.89
b. 0.89
c. -1.02
*d. 1.02
e. -2.37
180. If the area to the right of a value of
z (z has a standard normal distribution) is 0.0089, what is the value of z?
a. -0.89
b. 0.89
c. -1.02
d. 1.02
*e. 2.37
181. If P(Z > z) = 0.6844 what is the
value of z (z has a standard normal distribution)?
*a. -0.48
b. 0.48
c. -1.04
d. 1.04
e. -0.21
182. If P(Z < z) = 0.6844 what is the
value of z (z has a standard normal distribution)?
a. -0.48
*b. 0.48
c. -1.04
d. 1.04
e. -0.21
183. If P(Z > z) = 0.8508 what is the
value of z (z has a standard normal distribution)?
a. -0.48
b. 0.48
*c. -1.04
d. 1.04
e. -0.21
184. If P(Z < z) = 0.8508 what is the
value of z (z has a standard normal distribution)?
a. -0.48
b. 0.48
c. -1.04
*d. 1.04
e. -0.21
185. If P(Z > z) = 0.5832 what is the
value of z (z has a standard normal distribution)?
a. -0.48
b. 0.48
c. -1.04
d. 1.04
*e. -0.21
186. If P(Z < z) = 0.5832 what is the
value of z (z has a standard normal distribution)?
a. -0.48
b. 0.48
c. -1.04
d. 1.04
*e. 0.21
187. If P(Z > z) = 0.9830 what is the
value of z (z has a standard normal distribution)?
*a. -2.12
b. 2.12
c. -1.77
d. 1.77
e. -0.21
188. If P(Z < z) = 0.9830 what is the
value of z (z has a standard normal distribution)?
a. -2.12
*b. 2.12
c. -1.77
d. 1.77
e. -0.21
189. If P(Z > z) = 0.9616 what is the
value of z (z has a standard normal distribution)?
a. -2.12
b. 2.12
*c. -1.77
d. 1.77
e. -0.21
190. If P(Z < z) = 0.9616 what is the
value of z (z has a standard normal distribution)?
a. -2.12
b. 2.12
c. -1.77
*d. 1.77
e. -0.21
191. Given that z is a standard normal random variable and
that the area to the left of z is 0.305, then the value of z is:
a. 0.51
*b. -0.51
c. 0.86
d. -0.86
e. 0.24
192. 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. The
smallest 10% of oranges (those with the smallest diameters) cannot be sold and
are therefore given away. What is the cut-off
diameter in this case if oranges with the smallest 10% of diameters are to be
given away?
*a. 107.2
b. 103.6
c. 111.6
d. 109.6
e. 105.9
193. 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. The
smallest 5% of oranges (those with the smallest diameters) cannot be sold and
are therefore given away. What is the
cut-off diameter in this case if oranges with the smallest 5% of diameters are
to be given away?
a. 107.2
*b. 103.6
c. 111.6
d. 109.6
e. 105.9
194. 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. The
smallest 20% of oranges (those with the smallest diameters) cannot be sold and
are therefore given away. What is the
cut-off diameter in this case if oranges with the smallest 20% of diameters are
to be given away?
a. 107.2
b. 103.6
*c. 111.6
d. 109.6
e. 105.9
195. 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. The
smallest 15% of oranges (those with the smallest diameters) cannot be sold and
are therefore given away. What is the
cut-off diameter in this case if oranges with the smallest 15% of diameters are
to be given away?
a. 107.2
b. 103.6
c. 111.6
*d. 109.6
e. 105.9
196. 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. The
smallest 8% of oranges (those with the smallest diameters) cannot be sold and
are therefore given away. What is the
cut-off diameter in this case if oranges with the smallest 8% of diameters are
to be given away?
a. 107.2
b. 103.6
c. 111.6
d. 109.6
*e. 105.9
197. 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. The farmer
would like to select the largest 10% of oranges (those with the largest
diameters) in order to be able to keep them for himself and his family to
enjoy! What is the cut-off diameter in
this case if oranges with the largest 10% of diameters are to be kept?
*a. 132.8
b. 136.4
c. 128.4
d. 130.4
e. 134.1
198. 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. The farmer
would like to select the largest 5% of oranges (those with the largest
diameters) in order to be able to keep them for himself and his family to
enjoy! What is the cut-off diameter in
this case if oranges with the largest 5% of diameters are to be kept?
a. 132.8
*b. 136.4
c. 128.4
d. 130.4
e. 134.1
199. 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. The farmer
would like to select the largest 20% of oranges (those with the largest
diameters) in order to be able to keep them for himself and his family to
enjoy! What is the cut-off diameter in
this case if oranges with the largest 20% of diameters are to be kept?
a. 132.8
b. 136.4
*c. 128.4
d. 130.4
e. 134.1
200. 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. The farmer
would like to select the largest 15% of oranges (those with the largest
diameters) in order to be able to keep them for himself and his family to
enjoy! What is the cut-off diameter in
this case if oranges with the largest 15% of diameters are to be kept?
a. 132.8
b. 136.4
c. 128.4
*d. 130.4
e. 134.1
201. 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. The farmer
would like to select the largest 8% of oranges (those with the largest
diameters) in order to be able to keep them for himself and his family to
enjoy! What is the cut-off diameter in
this case if oranges with the largest 8% of diameters are to be kept?
a. 132.8
b. 136.4
c. 128.4
d. 130.4
*e. 134.1
202. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours.
Printers are to be sold with a guarantee. The manufacturer of the printers wants only
5% of printers to fail before the guarantee period is up. What number of hours should the guarantee
period be set at so that only 5% of printers fail before this time?
*a. 1171 hours
b. 1244 hours
c. 1205 hours
d. 1124 hours
e. 1089 hours
203. The time until first failure of a brand
of inkjet printers is normally distributed with a mean of 1500 hours and a
standard deviation of 200 hours.
Printers are to be sold with a guarantee. The manufacturer of the printers wants only
10% of printers to fail before the guarantee period is up. What number of hours should the guarantee
period be set at so that only 10% of printers fail before this time?
a. 1171 hours
*b. 1244 hours
c. 1205 hours
d. 1124 hours
e. 1089 hours
204. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours.
Printers are to be sold with a guarantee. The manufacturer of the printers wants only
7% of printers to fail before the guarantee period is up. What number of hours should the guarantee
period be set at so that only 7% of printers fail before this time?
a. 1171 hours
b. 1244 hours
*c. 1205 hours
d. 1124 hours
e. 1089 hours
205. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours.
Printers are to be sold with a guarantee. The manufacturer of the printers wants only
3% of printers to fail before the guarantee period is up. What number of hours should the guarantee
period be set at so that only 3% of printers fail before this time?
a. 1171 hours
b. 1244 hours
c. 1205 hours
*d. 1124 hours
e. 1089 hours
206. The time until first failure of a
brand of inkjet printers is normally distributed with a mean of 1500 hours and
a standard deviation of 200 hours.
Printers are to be sold with a guarantee. The manufacturer of the printers wants only
2% of printers to fail before the guarantee period is up. What number of hours should the guarantee
period be set at so that only 2% of printers fail before this time?
a. 1171 hours
b. 1244 hours
c. 1205 hours
d. 1124 hours
*e. 1089 hours
207. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
*a. R196,449
b. R192,816
c. R190,364
d. R198,808
e. R203,263
208. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R196,449
*b. R192,816
c. R190,364
d. R198,808
e. R203,263
209. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R196,449
b. R192,816
*c. R190,364
d. R198,808
e. R203,263
210. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R196,449
b. R192,816
c. R190,364
*d. R198,808
e. R203,263
211. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R196,449
b. R192,816
c. R190,364
d. R198,808
*e. R203,263
212. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
*a. R163,551
b. R167,184
c. R169,636
d. R161,192
e. R156,737
213. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R163,551
*b. R167,184
c. R169,636
d. R161,192
e. R156,737
214. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R163,551
b. R167,184
*c. R169,636
d. R161,192
e. R156,737
215. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R163,551
b. R167,184
c. R169,636
*d. R161,192
e. R156,737
216. The starting annual salaries of newly
qualified chartered accountants (CA’s) in South Africa
a. R163,551
b. R167,184
c. R169,636
d. R161,192
*e. R156,737
217. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. If only
the shortest 10% of students are to be selected to perform a specific task,
what is the cut-off height?
a. 178.4cm
b. 123.5cm
*c. 165.6cm
d. 145.7cm
e. 159.2cm
218. In a large statistics class the
heights of the students are normally distributed with a mean of 172cm and a
variance of 25cm2. If only
the tallest 10% of students are to be selected to perform a specific task, what
is the cut-off height?
*a. 178.4cm
b. 123.5cm
c. 165.6cm
d. 145.7cm
e. 159.2cm
219. 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 is the length of a particular call (in seconds) if only 1% of
calls are shorter?
*a. 146.95
b. 157.85
c. 174.21
d. 333.05
e. 305.79
220. 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 is the length of a particular call (in seconds) if only 2% of
calls are shorter?
a. 146.95
*b. 157.85
c. 174.21
d. 333.05
e. 305.79
221. 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 is the length of a particular call (in seconds) if only 5% of
calls are shorter?
a. 146.95
b. 157.85
*c. 174.21
d. 333.05
e. 305.79
222. 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 is the length of a particular call (in seconds) if only 1% of calls are
longer?
a. 146.95
b. 157.85
c. 174.21
*d. 333.05
e. 305.79
223. 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 is the length of a particular call (in seconds) if only 5% of
calls are longer?
a. 146.95
b. 157.85
c. 174.21
d. 333.05
*e. 305.79
224. If X ~ N(μ, 25) and p(X > 12) =
0.3446. What is the value of μ?
*a. 10.00
b. 5.90
c. 1.80
d. 8.05
e. 4.65
225. If X ~ N(μ, 25) and p(X > 12) =
0.1112. What is the value of μ?
a. 10.00
*b. 5.90
c. 1.80
d. 8.05
e. 4.65
226. If X ~ N(μ, 25) and p(X > 12) =
0.0207. What is the value of μ?
a. 10.00
b. 5.90
*c. 1.80
d. 8.05
e. 4.65
227. If X ~ N(μ, 25) and p(X > 12) =
0.2148. What is the value of μ?
a. 10.00
b. 5.90
c. 1.80
*d. 8.05
e. 4.65
228. If X ~ N(μ, 25) and p(X > 12) =
0.0708. What is the value of μ?
a. 10.00
b. 5.90
c. 1.80
d. 8.05
*e. 4.65
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