Statistics MCQs –Continuous Distributions Part 11
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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
Answer: E
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
Answer: A
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
Answer: B
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
Answer: C
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
Answer: D
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
Answer: E
207. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the minimum annual salary earned by the top 5% of newly qualified CA’s?
a. R196,449
b. R192,816
c. R190,364
d. R198,808
e. R203,263
Answer: A
208. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the minimum annual salary earned by the top 10% of newly qualified CA’s?
a. R196,449
b. R192,816
c. R190,364
d. R198,808
e. R203,263
Answer: B
209. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the minimum annual salary earned by the top 15% of newly qualified CA’s?
a. R196,449
b. R192,816
c. R190,364
d. R198,808
e. R203,263
Answer: C
210. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the minimum annual salary earned by the top 3% of newly qualified CA’s?
a. R196,449
b. R192,816
c. R190,364
d. R198,808
e. R203,263
Answer: D
211. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the minimum annual salary earned by the top 1% of newly qualified CA’s?
a. R196,449
b. R192,816
c. R190,364
d. R198,808
e. R203,263
Answer: E
212. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the maximum annual salary earned by the 5% of newly qualified CA’s with the lowest salaries?
a. R163,551
b. R167,184
c. R169,636
d. R161,192
e. R156,737
Answer: A
213. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the maximum annual salary earned by the 10% of newly qualified CA’s with the lowest salaries?
a. R163,551
b. R167,184
c. R169,636
d. R161,192
e. R156,737
Answer: B
214. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the maximum annual salary earned by the 15% of newly qualified CA’s with the lowest salaries?
a. R163,551
b. R167,184
c. R169,636
d. R161,192
e. R156,737
Answer: C
215. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the maximum annual salary earned by the 3% of newly qualified CA’s with the lowest salaries?
a. R163,551
b. R167,184
c. R169,636
d. R161,192
e. R156,737
Answer: D
216. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the maximum annual salary earned by the 1% of newly qualified CA’s with the lowest salaries?
a. R163,551
b. R167,184
c. R169,636
d. R161,192
e. R156,737
Answer: E
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
Answer: C
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
Answer: A
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
Answer: A
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
Answer: B