# Statistics MCQs – Discrete Distributions Part 12

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221. Cars arrive at a tollgate at an average rate of 12 cars per hour. If a fee of R5.50 is required per car to be allowed to pass through the tollgate, what are the expected earnings of the tollgate in a 8-hour period?

a. R792

b. R936

c. R528

d. R660

e. R1584

Answer: C

222. Cars arrive at a tollgate at an average rate of 10 cars per hour. If a fee of R5.50 is required per car to be allowed to pass through the tollgate, what are the expected earnings of the tollgate in a 12-hour period?

a. R792

b. R936

c. R528

d. R660

e. R1584

Answer: D

223. Cars arrive at a tollgate at an average rate of 12 cars per hour. If a fee of R5.50 is required per car to be allowed to pass through the tollgate, what are the expected earnings of the tollgate in a 24-hour period?

a. R792

b. R936

c. R528

d. R660

e. R1584

Answer: E

224. X is a random variable such that X ~P (4) . What is the standard deviation of X?

a. 2

b. 4

c. 3

d. 5

e. 10

Answer: A

225. X is a random variable such that X ~P (16) . What is the standard deviation of X?

a. 2

b. 4

c. 3

d. 5

e. 10

Answer: B

226. X is a random variable such that X ~P (9) . What is the standard deviation of X?

a. 2

b. 4

c. 3

d. 5

e. 10

Answer: C

227. X is a random variable such that X ~P (25) . What is the standard deviation of X?

a. 2

b. 4

c. 3

d. 5

e. 10

Answer: D

228. X is a random variable such that X ~P (100) . What is the standard deviation of X?

a. 2

b. 4

c. 3

d. 5

e. 10

Answer: E

229. Cars arrive at a BP petrol station at an average rate of 32 cars per hour. What is the standard deviation of the number of cars that arrive within half an hour?

a. 4

b. 16

c. 2

d. 5

e. 25

Answer: A

230. Cars arrive at a BP petrol station at an average rate of 32 cars per hour. What is the variance of the number of cars that arrive within half an hour?

a. 4

b. 16

c. 2

d. 5

e. 25

Answer: B

231. Cars arrive at a BP petrol station at an average rate of 16 cars per hour. What is the standard deviation of the number of cars that arrive within quarter of an hour?

a. 4

b. 16

c. 2

d. 5

e. 25

Answer: C

232. Cars arrive at a BP petrol station at an average rate of 50 cars per hour. What is the standard deviation of the number of cars that arrive within half an hour?

a. 4

b. 16

c. 2

d. 5

e. 25

Answer: D

233. Cars arrive at a BP petrol station at an average rate of 50 cars per hour. What is the variance of the number of cars that arrive within half an hour?

a. 4

b. 16

c. 2

d. 5

e. 25

Answer: E

234. A local police station receives on average 8 emergency telephone calls per hour. What is the standard deviation of the number of calls received in half an hour?

a. 4.00

b. 16.0

c. 8.00

d. 2.83

e. 2.00

Answer: E

235. In a public library, books are lost and have to be replaced at an average rate of 2.75 books per week. What is the variance of the number of books lost in a two-week period?

a. 2.75

b. 11.00

c. 5.50

d. 8.25

e. none of the above

Answer: C

236. Which of the following cannot be modelled by a Poisson distribution?

a. The number of children watching a movie at a given point in time

b. The number of telephone calls received by a switchboard in an hour

c. The number of customers arriving at a petrol station on Christmas day

d. The number of bacteria found per square metre of soil

e. The number of patients arriving at a hospital in a week

Answer: A