# Statistics MCQs – Continuous Distributions Part 4

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61. If X ~U (15,19) , what is the variance of X?

a. 3.00

b. 1.33

c. 2.08

d. 4.08

e. 0.75

Answer: B

62. If X ~U (11,16) , what is the variance of X?

a. 3.00

b. 1.33

c. 2.08

d. 4.08

e. 0.75

Answer: C

63. If X ~U (13,20) , what is the variance of X?

a. 3.00

b. 1.33

c. 2.08

d. 4.08

e. 0.75

Answer: D

64. If X ~U (14,17) , what is the variance of X?

a. 3.00

b. 1.33

c. 2.08

d. 4.08

e. 0.75

Answer: E

65. The length of time it takes to wait in the queue on registration day at a certain university is uniformly distributed between 10 minutes and 2 hours. What is the variance of the waiting time?

a. 1008 minutes^{2}

b. 31.8 minutes

c. 65 minutes^{2}

d. 100 minutes^{2}

e. 25 minutes

Answer: A

66. The length of time it takes to wait in the queue on registration day at a certain university is uniformly distributed between 10 minutes and 2 hours. What is the standard deviation of the waiting time?

a. 1008 minutes^{2}

b. 31.8 minutes

c. 65 minutes^{2}

d. 100 minutes^{2}

e. 25 minutes

Answer: B

67. The mass of a 1000g container of yoghurt is equally likely to take on any value in the interval (995g, 1010g) . The container will not contain less than 995g or more than 1010g of yoghurt. What is the expected mass of the yoghurt container?

a. 1000g

b. 1002.5g

c. 1010g

d. 995g

e. 1005g

Answer: B

68. The mass of a 1000g container of yoghurt is equally likely to take on any value in the interval (995g, 1010g) . The container will not contain less than 995g or more than 1010g of yoghurt. What is the standard deviation of the mass of the yoghurt container?

a. 18.75g

b. 21.46g

c. 2.15g

d. 4.33g

e. 3.43g

Answer: D

69. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. A student arrives at university 10 minutes before the scheduled start of her first lecture. What is the probability that it will take the student more than 10 minutes to find a parking space, causing her to be late for her lecture?

a. 0.082

b. 0.024

c. 0.287

d. 0.135

e. 0.368

Answer: A

70. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. A student arrives at university 15 minutes before the scheduled start of her first lecture. What is the probability that it will take the student more than 15 minutes to find a parking space, causing her to be late for her lecture?

a. 0.082

b. 0.024

c. 0.287

d. 0.135

e. 0.368

Answer: B

71. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. A student arrives at university 5 minutes before the scheduled start of her first lecture. What is the probability that it will take the student more than 5 minutes to find a parking space, causing her to be late for her lecture?

a. 0.082

b. 0.024

c. 0.287

d. 0.135

e. 0.368

Answer: C

72. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 5 minutes. A student arrives at university 10 minutes before the scheduled start of her first lecture. What is the probability that it will take the student more than 10 minutes to find a parking space, causing her to be late for her lecture?

a. 0.082

b. 0.024

c. 0.287

d. 0.135

e. 0.368

Answer: D

73. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 5 minutes. A student arrives at university 5 minutes before the scheduled start of her first lecture. What is the probability that it will take the student more than 5 minutes to find a parking space, causing her to be late for her lecture?

a. 0.082

b. 0.024

c. 0.287

d. 0.135

e. 0.368

Answer: E

74. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. What is the probability that it takes a randomly selected student between 2 and 12 minutes to find a parking space in the parking lot?

a. 0.557

b. 0.524

c. 0.471

d. 0.233

e. 0.204

Answer: A

75. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. What is the probability that it takes a randomly selected student between 2 and 10 minutes to find a parking space in the parking lot?

a. 0.557

b. 0.524

c. 0.471

d. 0.233

e. 0.204

Answer: B

76. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. What is the probability that it takes a randomly selected student between 2 and 8 minutes to find a parking space in the parking lot?

a. 0.557

b. 0.524

c. 0.471

d. 0.233

e. 0.204

Answer: C

77. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. What is the probability that it takes a randomly selected student between 4 and 8 minutes to find a parking space in the parking lot?

a. 0.557

b. 0.524

c. 0.471

d. 0.233

e. 0.204

Answer: D

78. Let X represent the amount of time it takes a student to find a parking space in the parking lot at a university. We know that the distribution of X can be modelled using an exponential distribution with a mean of 4 minutes. What is the probability that it takes a randomly selected student between 5 and 10 minutes to find a parking space in the parking lot?

a. 0.557

b. 0.524

c. 0.471

d. 0.233

e. 0.204

Answer: E

79. A small bank branch has a single teller to handle transactions with customers. Customers arrive at the bank at an average rate of one every three minutes. What is the probability that it will be more than 10 minutes before the first customer arrives for the day after the bank has opened at 8am?

a. 0.036

b. 0.189

c. 0.368

d. 0.097

e. 0.018

Answer: A

80. A small bank branch has a single teller to handle transactions with customers. Customers arrive at the bank at an average rate of one every three minutes. What is the probability that it will be more than 5 minutes before the first customer arrives for the day after the bank has opened at 8am?

a. 0.036

b. 0.189

c. 0.368

d. 0.097

e. 0.018

Answer: B