# Statistics MCQs – Continuous Distributions Part 3

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41. Everyday you make the trip from your home to work by car. The travel time to work from home is equally likely to be anywhere between 10 minutes and 25 minutes, but is never less than 10 minutes or more than 25 minutes. What is the probability that on a randomly selected day it takes you more than 20 minutes to travel to work from home?

a. 1.000

b. 0.333

c. 0.500

d. 0.667

e. 0.000

Answer: B

42. Everyday you make the trip from your home to work by car. The travel time to work from home is equally likely to be anywhere between 10 minutes and 25 minutes, but is never less than 10 minutes or more than 25 minutes. What is the probability that on a randomly selected day it takes you more than 15 minutes to travel to work from home?

a. 1.000

b. 0.333

c. 0.500

d. 0.667

e. 0.000

Answer: D

43. The temperature in your office at work is regulated by a thermostat and is equally likely to be between 17 degrees Celsius and 23 degrees Celsius, but is never more than 23 or less than 17 degrees. What is the probability that at a randomly selected point in time, the temperature in your office is more than 21 degrees?

a. 0.333

b. 0.500

c. 0.667

d. 0.015

e. 0.833

Answer: A

44. The temperature in your office at work is regulated by a thermostat and is equally likely to be between 17 degrees Celsius and 23 degrees Celsius, but is never more than 23 or less than 17 degrees. What is the probability that at a randomly selected point in time, the temperature in your office is more than 18 degrees?

a. 0.333

b. 0.500

c. 0.667

d. 0.015

e. 0.833

Answer: E

45. The temperature in your office at work is regulated by a thermostat and is equally likely to be between 17 degrees Celsius and 23 degrees Celsius, but is never more than 23 or less than 17 degrees. What is the probability that at a randomly selected point in time, the temperature in your office is less than 21 degrees?

a. 0.333

b. 0.500

c. 0.667

d. 0.015

e. 0.833

Answer: C

46. The length of time patients must wait to see a doctor at an emergency room of a large hospital is uniformly distributed between 40 minutes and 3 hours. What is the expected waiting time for patients to see a doctor?

a. 110 minutes

b. 80 minutes

c. 95 minutes

d. 60 minutes

e. 100 minutes

Answer: A

47. The length of time patients must wait to see a doctor at an emergency room of a large hospital is uniformly distributed between 40 minutes and 2 hours. What is the expected waiting time for patients to see a doctor?

a. 110 minutes

b. 80 minutes

c. 95 minutes

d. 60 minutes

e. 100 minutes

Answer: B

48. The length of time patients must wait to see a doctor at an emergency room of a large hospital is uniformly distributed between 40 minutes and 2.5 hours. What is the expected waiting time for patients to see a doctor?

a. 110 minutes

b. 80 minutes

c. 95 minutes

d. 60 minutes

e. 100 minutes

Answer: C

49. The length of time patients must wait to see a doctor at an emergency room of a large hospital is uniformly distributed between 30 minutes and 1.5 hours. What is the expected waiting time for patients to see a doctor?

a. 110 minutes

b. 80 minutes

c. 95 minutes

d. 60 minutes

e. 100 minutes

Answer: D

50. The length of time patients must wait to see a doctor at an emergency room of a large hospital is uniformly distributed between 50 minutes and 2.5 hours. What is the expected waiting time for patients to see a doctor?

a. 110 minutes

b. 80 minutes

c. 95 minutes

d. 60 minutes

e. 100 minutes

Answer: E

51. In a popular shopping centre, the waiting time for an ABSA ATM machine is found to be uniformly distributed between 1 and 5 minutes. What is the expected waiting time (in minutes) for the ATM to be free to use?

a. 2 minutes

b. 5 minutes

c. 3 minute

d. 4 minutes

e. 0.25 minutes

Answer: C

52. In a popular shopping centre, the waiting time for an ABSA ATM machine is found to be uniformly distributed between 1 and 9 minutes. What is the expected waiting time (in minutes) for the ATM to be free to use?

a. 2 minutes

b. 5 minutes

c. 3 minute

d. 4 minutes

e. 0.25 minutes

Answer: B

53. In a popular shopping centre, the waiting time for an ABSA ATM machine is found to be uniformly distributed between 1 and 7 minutes. What is the expected waiting time (in minutes) for the ATM to be free to use?

a. 2 minutes

b. 5 minutes

c. 3 minute

d. 4 minutes

e. 0.25 minutes

Answer: D

54. If the continuous random variable X is uniformly distributed over the interval [15,20] then the mean of X is:

a. 17.5

b. 15

c. 25

d. 35

e. none of the above

Answer: A

55. If X ~U (12,18) , what is the standard deviation of X?

a. 1.73

b. 1.15

c. 1.44

d. 2.02

e. 0.87

Answer: A

56. If X ~U (15,19) , what is the standard deviation of X?

a. 1.73

b. 1.15

c. 1.44

d. 2.02

e. 0.87

Answer: B

57. If X ~U (11,16) , what is the standard deviation of X?

a. 1.73

b. 1.15

c. 1.44

d. 2.02

e. 0.87

Answer: C

58. If X ~U (13,20) , what is the standard deviation of X?

a. 1.73

b. 1.15

c. 1.44

d. 2.02

e. 0.87

Answer: D

59. If X ~U (14,17) , what is the standard deviation of X?

a. 1.73

b. 1.15

c. 1.44

d. 2.02

e. 0.87

Answer: E

60. If X ~U (12,18) , what is the variance of X?

a. 3.00

b. 1.33

c. 2.08

d. 4.08

e. 0.75

Answer: A