# Statistics MCQs – Discrete Distributions Part 9

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161. 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 three or fewer colonies?

a. 0.238

b. 0.433

c. 0.125

d. 0.265

e. 0.285

Answer: D

162. 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 six colonies per dish. What is the probability that the next dish studied will contain four or fewer colonies?

a. 0.238

b. 0.433

c. 0.125

d. 0.265

e. 0.285

Answer: E

163. A random variable, X, follows a Poisson distribution with a standard deviation of 3. What is P (X < 5) ?

a. 0.055

b. 0.815

c. 0.238

d. 0.440

e. 0.151

Answer: A

164. A random variable, X, follows a Poisson distribution with a variance of 3. What is P (X < 5) ?

a. 0.055

b. 0.815

c. 0.238

d. 0.440

e. 0.151

Answer: B

165. A random variable, X, follows a Poisson distribution with a standard deviation of 2. What is P (X < 3) ?

a. 0.055

b. 0.815

c. 0.238

d. 0.440

e. 0.151

Answer: C

166. A random variable, X, follows a Poisson distribution with a variance of 5. What is P (X < 5) ?

a. 0.055

b. 0.815

c. 0.238

d. 0.440

e. 0.151

Answer: D

167. A random variable, X, follows a Poisson distribution with a variance of 6. What is P (X < 4) ?

a. 0.055

b. 0.815

c. 0.238

d. 0.440

e. 0.151

Answer: E

168. If X is a random variable such that X ~P (3.5) , what is P (X ⩽ 5) ?

a. 0.858

b. 0.321

c. 0.446

d. 0.062

e. 0.529

Answer: A

169. If X is a random variable such that X ~P (3.5) , what is P (X ⩽ 2) ?

a. 0.858

b. 0.321

c. 0.446

d. 0.062

e. 0.529

Answer: B

170. If X is a random variable such that X ~P (6) , what is P (X ⩽ 5) ?

a. 0.858

b. 0.321

c. 0.446

d. 0.062

e. 0.529

Answer: C

171. If X is a random variable such that X ~P (6) , what is P (X ⩽ 2) ?

a. 0.858

b. 0.321

c. 0.446

d. 0.062

e. 0.529

Answer: D

172. If X is a random variable such that X ~P (5.5) , what is P (X ⩽ 5) ?

a. 0.858

b. 0.321

c. 0.446

d. 0.062

e. 0.529

Answer: E

173. Cars arrive at an Engen petrol station at an average rate of 10 cars per hour. What is the probability that less than 4 cars arrive in 30 minutes?

a. 0.265

b. 0.433

c. 0.857

d. 0.532

e. 0.406

Answer: A

174. Cars arrive at an Engen petrol station at an average rate of 8 cars per hour. What is the probability that less than 4 cars arrive in 30 minutes?

a. 0.265

b. 0.433

c. 0.857

d. 0.532

e. 0.406

Answer: B

175. Cars arrive at an Engen petrol station at an average rate of 6 cars per hour. What is the probability that less than 4 cars arrive in 20 minutes?

a. 0.265

b. 0.433

c. 0.857

d. 0.532

e. 0.406

Answer: C

176. Cars arrive at an Engen petrol station at an average rate of 9 cars per hour. What is the probability that less than 5 cars arrive in 30 minutes?

a. 0.265

b. 0.433

c. 0.857

d. 0.532

e. 0.406

Answer: D

177. Cars arrive at an Engen petrol station at an average rate of 12 cars per hour. What is the probability that less than 2 cars arrive in 10 minutes?

a. 0.265

b. 0.433

c. 0.857

d. 0.532

e. 0.406

Answer: E

178. A local police station receives on average 8 emergency telephone calls per hour. What is the probability that the station will get at least 4 calls per hour?

a. 0.039

b. 0.094

c. 0.905

d. 0.958

e. 0.963

Answer: D

179. Seventy (70) accidents are reported on a particular stretch of highway over a 90-day period. What is the probability that there will be more than one accident during a week (assume a seven-day week) ?

a. 0.9722

b. 0.9857

c. 0.9561

d. 0.9756

e. 0.9844

Answer: A

180. Eighty (80) accidents are reported on a particular stretch of highway over a 90-day period. What is the probability that there will be more than one accident during a week (assume a seven-day week) ?

a. 0.9722

b. 0.9857

c. 0.9561

d. 0.9756

e. 0.9844

Answer: B