# Statistics MCQs –Discrete Distributions Part 10

Glide to success with Doorsteptutor material for CAT : fully solved questions with step-by-step explanation- practice your way to success.

181. Seventy (70) accidents are reported on a particular stretch of highway over a 100-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: C

182. Eighty (80) accidents are reported on a particular stretch of highway over a 100-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: D

183. Seventy (70) accidents are reported on a particular stretch of highway over a 80-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: E

184. 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 at least two colonies?

a. 0.908

b. 0.762

c. 0.960

d. 0.875

e. 0.849

Answer: A

185. 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 at least three colonies?

a. 0.908

b. 0.762

c. 0.960

d. 0.875

e. 0.849

Answer: B

186. 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 at least two colonies?

a. 0.908

b. 0.762

c. 0.960

d. 0.875

e. 0.849

Answer: C

187. 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 at least three colonies?

a. 0.908

b. 0.762

c. 0.960

d. 0.875

e. 0.849

Answer: D

188. 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 at least four colonies?

a. 0.908

b. 0.762

c. 0.960

d. 0.875

e. 0.849

Answer: E

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

a. 0.884

b. 0.084

c. 0.567

d. 0.384

e. 0.715

Answer: A

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

a. 0.884

b. 0.084

c. 0.567

d. 0.384

e. 0.715

Answer: B

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

a. 0.884

b. 0.084

c. 0.567

d. 0.384

e. 0.715

Answer: C

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

a. 0.884

b. 0.084

c. 0.567

d. 0.384

e. 0.715

Answer: D

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

a. 0.884

b. 0.084

c. 0.567

d. 0.384

e. 0.715

Answer: E

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

a. 0.275

b. 0.864

c. 0.715

d. 0.983

e. 0.642

Answer: A

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

a. 0.275

b. 0.864

c. 0.715

d. 0.983

e. 0.642

Answer: B

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

a. 0.275

b. 0.864

c. 0.715

d. 0.983

e. 0.642

Answer: C

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

a. 0.275

b. 0.864

c. 0.715

d. 0.983

e. 0.642

Answer: D

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

a. 0.275

b. 0.864

c. 0.715

d. 0.983

e. 0.642

Answer: E

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

a. 0.560

b. 0.371

c. 0.053

d. 0.297

e. 0.323

Answer: A

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

a. 0.560

b. 0.371

c. 0.053

d. 0.297

e. 0.323

Answer: B