# 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

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 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

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

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

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

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

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

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

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

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

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

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