# Statistics MCQs –Discrete Distributions Part 8

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141. Assume that during the Cape Town Argus Pick ‘n Pay cycle tour accidents occur on average 3 times per 10 km stretch. What is the probability that it is more than 5 km before the next accident?

a. 0.777

b. 0.223

c. 0.741

d. 0.259

e. 0.521

Answer: B

142. Car accidents occur in South Africa at an average rate of 72 accidents per hour. What is the probability that it will be more than 3 minutes before the next accident occurs?

a. 0.877

b. 0.651

c. 0.131

d. 0.027

e. 0.584

Answer: D

143. A dispatcher for an airport shuttle will send a van to the airport on average twice per hour during the Soccer World Cup in 2010. The distribution is expected to be Poisson, and the driver must take a 15- minute lunch break. The probability that he can complete his lunch break before receiving a call is:

a. 0.135

b. 0.607

c. 0.394

d. 1.649

e. 0.865

Answer: B

144. A dispatcher for an airport shuttle will send a van to the airport on average twice per hour during the Soccer World Cup in 2010. The distribution is expected to be Poisson, and the driver must take a 15- minute lunch break. The probability that he gets 2 calls (dispatches) in 30 minutes is:

a. 0.184

b. 0.465

c. 0.234

d. 0.314

e. 0.000

Answer: A

145. 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 probability that in a given month (4 weeks) 10 books are lost?

a. 0.460

b. 0.119

c. 0.275

d. 0.435

e. 0.357

Answer: B

146. 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 probability that it will be more than one week before the next book is lost?

a. 0.690

b. 0.340

*c. 0.064

d. 0.284

e. 0.170

147. A drop of water from a lake contains on average 0.5 bacteria per drop. A small dish containing 4 drops of water from this lake is placed under the microscope. What is the probability of observing at most 1 bacterium in this dish?

a. 0.406

b. 0.594

c. 0.092

d. 0.938

e. 0.910

Answer: A

148. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted level. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 7.5 tickets per day. What is the probability that less than 6 tickets are written on a randomly selected day?

a. 0.241

b. 0.301

c. 0.378

d. 0.132

e. 0.450

Answer: A

149. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted level. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 7 tickets per day. What is the probability that less than 6 tickets are written on a randomly selected day?

a. 0.241

b. 0.301

c. 0.378

d. 0.132

e. 0.450

Answer: B

150. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted level. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 7.5 tickets per day. What is the probability that less than 7 tickets are written on a randomly selected day?

a. 0.241

b. 0.301

c. 0.378

d. 0.132

e. 0.450

Answer: C

151. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted level. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 7.5 tickets per day. What is the probability that less than 5 tickets are written on a randomly selected day?

a. 0.241

b. 0.301

c. 0.378

d. 0.132

e. 0.450

Answer: D

152. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted level. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 7 tickets per day. What is the probability that less than 7 tickets are written on a randomly selected day?

a. 0.241

b. 0.301

c. 0.378

d. 0.132

e. 0.450

Answer: E

153. A local motor vehicle break-down service must respond to, on average, 10 calls per day in order to keep revenues at the budgeted level. Suppose the number of calls received from customers per day follows a Poisson distribution with a mean of 11 calls per day. What is the probability that at most 10 calls will be received on a randomly selected day?

a. 0.460

b. 0.232

c. 0.347

d. 0.576

e. 0.689

Answer: A

154. A local motor vehicle break-down service must respond to, on average, 10 calls per day in order to keep revenues at the budgeted level. Suppose the number of calls received from customers per day follows a Poisson distribution with a mean of 11 calls per day. What is the probability that at most 8 calls will be received on a randomly selected day?

a. 0.460

b. 0.232

c. 0.347

d. 0.576

e. 0.689

Answer: B

155. A local motor vehicle break-down service must respond to, on average, 10 calls per day in order to keep revenues at the budgeted level. Suppose the number of calls received from customers per day follows a Poisson distribution with a mean of 12 calls per day. What is the probability that at most 10 calls will be received on a randomly selected day?

a. 0.460

b. 0.232

c. 0.347

d. 0.576

e. 0.689

Answer: C

156. A local motor vehicle break-down service must respond to, on average, 10 calls per day in order to keep revenues at the budgeted level. Suppose the number of calls received from customers per day follows a Poisson distribution with a mean of 12 calls per day. What is the probability that at most 12 calls will be received on a randomly selected day?

a. 0.460

b. 0.232

c. 0.347

d. 0.576

e. 0.689

Answer: D

157. A local motor vehicle break-down service must respond to, on average, 10 calls per day in order to keep revenues at the budgeted level. Suppose the number of calls received from customers per day follows a Poisson distribution with a mean of 11 calls per day. What is the probability that at most 12 calls will be received on a randomly selected day?

a. 0.460

b. 0.232

c. 0.347

d. 0.576

e. 0.689

Answer: E

158. In checking river water samples for bacteria, water is placed in a culture medium in order to grow colonies of bacteria. The number of colonies seen in a dish is a random variable, *X*. Scientists know that on average there are four colonies per dish. What is the probability that the next dish studied will contain two or fewer colonies?

a. 0.238

b. 0.433

c. 0.125

d. 0.265

e. 0.285

Answer: A

159. In checking river water samples for bacteria, water is placed in a culture medium in order to grow colonies of bacteria. The number of colonies seen in a dish is a random variable, *X*. Scientists know that on average there are four colonies per dish. What is the probability that the next dish studied will contain three or fewer colonies?

a. 0.238

b. 0.433

c. 0.125

d. 0.265

e. 0.285

Answer: B

160. In checking river water samples for bacteria, water is placed in a culture medium in order to grow colonies of bacteria. The number of colonies seen in a dish is a random variable, *X*. Scientists know that on average there are five colonies per dish. What is the probability that the next dish studied will contain two or fewer colonies?

a. 0.238

b. 0.433

c. 0.125

d. 0.265

e. 0.285

Answer: C