Quiz 5 Continuous Distributions

Quiz 1 Data and graphical descriptive statistics

Quiz 5 Continuous distributions1. Which of the following statements is not correct concerning the probability distribution of a continuous random variable?a. the vertical coordinate is the probability density function

b. the range of the random variable is found on the x-axis

c. the total area represented under the curve will equal 1

*d. the area under the curve between points a and b represents the probability that X = a

e. the area under the curve represents the sum of probabilities for all possible outcomes

2. Which of the following is not a characteristic of the normal distribution?

a. it is a symmetrical distribution

*b. the mean is always zero

c. the mean, median and mode are equal

d. it is a bell-shaped distribution

e. the area under the curve equals one

3. Which of the following is not a correct statement?a. the exponential distribution describes the Poisson process as a continuous random variable

b. the exponential distribution is a family of curves, which are completely described by the mean

*c. the mean of the exponential distribution is the inverse of the mean of the Poisson

d. the Poisson is a probability distribution for a discrete random variable while the exponential distribution is continuous

e. the area under the curve for an exponential distribution equals 1

4. Which of the following do the normal distribution and the exponential density function have in common?a. both are bell-shaped

b. both are symmetrical distributions

c. both approach infinity as x approaches infinity

*d. both approach zero as x approaches infinity

e. all of the above are features common to both distributions

5. Which of the following statement is not true for an exponential distribution with parameter ?

a. mean = 1 /

b. standard deviation = 1 /

c. the distribution is completely determined once the value of is known

d. the area under the curve is equal to one

*e. the distribution is a two-parameter distribution since the mean and standard deviation are equal

6. Which of the following distributions is suitable to model the length of time that elapses before the first employee passes through the security door of a company?

*a. exponential

b. normal

c. poisson

d. binomial

e. uniform

7. Which of the following distributions is suitable to measure the length of time that elapses between the arrival of cars at a petrol station pump?

a. normal

b. binomial

c. uniform

d. poisson

*e. exponential

8. A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all the questions randomly by guessing the answer to each question. Which of the following probability distributions can be used to calculate the students chance of getting at least 20 questions right?

*a.Binomial distribution

b. Poisson distribution

c. Exponential distribution

d. Uniform distributione. Normal distribution9. It is known that 20% of all vehicles parked on campus during the week do not have the required parking disk. A random sample of 10 cars is observed one Monday morning and X is the number in the sample that do not have the required parking disk. We can assume here that the probability distribution of X is:

*a. Binomial

b. Normal

c. Poisson

d. Exponential

e. Any continuous distribution will do

10. Which of the following statements is/are true regarding the normal distribution curve?

a. it is symmetrical

b. it is bell-shaped

c. it is asymptotic in that each end approaches the horizontal axis but never reaches it

d. its mean, median and mode are located at the same point

*e. all of the above statements are true

11. Indicate which of the statements below does not correctly apply to normal probability distributions:

a. they are all unimodal (ie: have a single mode)

b. they are all symmetrical

*c. they all have the same mean and standard deviation

d. the area under the probability curve is always equal to 1

e. for the standard normal distribution = 0 and = 1

12. Which of the following is not a characteristic of a binomial experiment?

a. there is a sequence of identical trials

*b. each trial results in two or more possible outcomes

c. the trials are independent of each other

d. the probability of success, p, is the same from one trial to another

e. all of the above are characteristics of a binomial experiment

13. Which probability distribution is appropriate for a count of events when the events of interest occur randomly, independently of one another and rarely?

a. normal distribution

b. exponential distribution

c. uniform distribution

*d. poisson distribution

e. binomial distribution

14. Which of the following cannot generate a Poisson distribution?

a. The number of cars arriving at a parking garage in a one-hour time interval

b. The number of telephone calls received in a ten-minute interval

*c. The number of customers arriving at a petrol station

d. The number of bacteria found in a cubic yard of soil

e. The number of misprints per page

15. The mean for the exponential distribution equals the mean for the Poisson distribution only when the former distribution has a mean equal to

*a. 1.0

b. 0.5

c. 0.25

d. 2.0

e. the means of the two distributions can never be equal

16. A larger standard deviation for a normal distribution with an unchanged mean indicates that the distribution becomes:

a. narrower and more peaked

*b. flatter and wider

c. more skewed to the right

d. more skewed to the left

e. a change in the standard deviation does not change the shape of the distribution

17. Which of the following statements regarding the probability density function, f(x), of the uniform distribution is correct?

a. the height of the density function differs for different values of X

b. the density function increases as the values of X increase

c. the density function is roughly bell-shaped

*d. the density function is constant for all values that X can assume

e. none of the above statements are true

18. Which of the following statements is correct?

a. The Exponential distribution is continuous and defined over the interval (-, )

*b. The mean of the Poisson distribution (with parameter ) equals the mean of the Exponential distribution (with parameter ) only when = = 1

c. It is impossible for a Normal distribution to have a negative population mean

d. The Binomial distribution has equal mean and variance only when p = 0.5

e. The Uniform distribution is a discrete probability distribution

19. 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 probability of waiting between 2 and 3 minutes to use the ATM?

*a. 0.25

b. 0.50

c. 0.75

d. 0.20

e. 0.40


a. 0.25

*b. 0.50

c. 0.75

d. 0.20

e. 0.40


a. 0.25

b. 0.50

*c. 0.75

d. 0.20

e. 0.40


a. 0.25

b. 0.50

c. 0.75

*d. 0.20

e. 0.40


a. 0.25

b. 0.50

c. 0.75

d. 0.20

*e. 0.40

24. 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 probability of being able to use the ATM in the first 30 seconds of waiting?

a. 0.25

b. 0.50

c. 0.75

d. 0.20

*e. 0.125

25. 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 probability that a patient will have to wait between 50 minutes and 2 hours to see a doctor?

*a. 0.500b. 0.286

c. 0.643

d. 0.786

e. 0.714

26. 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 probability that a patient will have to wait between 50 minutes and 1.5 hours to see a doctor?

a. 0.500

*b. 0.286

c. 0.643

d. 0.786

e. 0.714

27. 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 probability that a patient will have to wait between 30 minutes and 2 hours to see a doctor?

a. 0.500

b. 0.286

*c. 0.643

d. 0.786

e. 0.714


a. 0.500

b. 0.286

c. 0.643

*d. 0.786

e. 0.714


a. 0.500

b. 0.286

c. 0.643

d. 0.786

*e. 0.714

30. A train arrives at a station every 20 minutes. What is the probability that a person arriving at the station will have to wait less than half an hour for the next train?

a. 0.524

b. 0.237

c. 0.500

*d. 1.000

e. 0.872

31. In a small town the town hall clock strikes every half an hour. If you wake up at random during the middle of the night, what is the probability that you will have to wait less than 5 minutes before hearing the clock strike again?

a. 0.500

*b. 0.167

c. 0.833

d. 0.457

e. 0.138

32. It is known that the amount of apple juice found in 500ml bottle is uniformly distributed between 495ml and 510ml. What is the probability that a randomly selected bottle of apple juice contains less than 500ml of juice?

*a. 0.333

b. 0.667

c. 0.500

d. 0.000

e. 1.000

33. It is known that the amount of apple juice found in 500ml bottle is uniformly distributed between 495ml and 510ml. What is the probability that a randomly selected bottle of apple juice contains more than 500ml of juice?

a. 0.333

*b. 0.667

c. 0.500

d. 0.000

e. 1.000

34. 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 probability that a randomly chosen container of yoghurt has a mass of less than 1000g?*a. 0.333

b. 0.667

c. 0.500

d. 0.000

e. 1.00035. An investor knows that his portfolio is equally likely to yield an annual return anywhere in the interval [5%, 35%]. What is the probability that he will earn more than 13.5% in the forthcoming year?

*a. 0.72b. 0.50

c. 0.42

d. 0.17

e. 0.83

36. An investor knows that his portfolio is equally likely to yield an annual return anywhere in the interval [5%, 35%]. What is the probability that he will earn more than 20% in the forthcoming year?

a. 0.72

*b. 0.50

c. 0.42

d. 0.17

e. 0.83

37. An investor knows that his portfolio is equally likely to yield an annual return anywhere in the interval [5%, 35%]. What is the probability that he will earn more than 22.5% in the forthcoming year?

a. 0.72

b. 0.50

*c. 0.42

d. 0.17

e. 0.83


a. 0.72

b. 0.50

c. 0.42

*d. 0.17

e. 0.83


a. 0.72

b. 0.50

c. 0.42

d. 0.17

*e. 0.83

40. The distance between Cape Town and Hermanus is 120km. You are travelling towards Hermanus (from Cape Town) and you have been dropped off at some point along the highway between Cape Town and Hermanus. The only information known to you is that you have passed the half-way mark to Hermanus. What is the probability that you still have more than 30km to travel?

a. 0.625

b. 0.375

c. 0.750

d. 0.666

*e. 0.500

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

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

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

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

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

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 minutesc. 95 minutes

d. 60 minutes

e. 100 minutes

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

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


a. 110 minutes

b. 80 minutes

c. 95 minutes

*d. 60 minutes

e. 100 minutes


a. 110 minutes

b. 80 minutes

c. 95 minutes

d. 60 minutes

*e. 100 minutes

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


a. 2 minutes

*b. 5 minutes

c. 3 minute

d. 4 minutes

e. 0.25 minutes


a. 2 minutes

b. 5 minutes

c. 3 minute

*d. 4 minutes

e. 0.25 minutes

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

*a. 17.5b. 15

c. 25

d. 35

e. none of the above

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

*a. 1.73b. 1.15

c. 1.44

d. 2.02

e. 0.87


a. 1.73

*b. 1.15

c. 1.44

d. 2.02

e. 0.87


a. 1.73

b. 1.15

*c. 1.44

d. 2.02

e. 0.87


a. 1.73

b. 1.15

c. 1.44

*d. 2.02

e. 0.87


a. 1.73

b. 1.15

c. 1.44

d. 2.02

*e. 0.87

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

*a. 3.00b. 1.33c. 2.08d. 4.08e. 0.7561. If X ~ U(15, 19), what is the variance of X?

a. 3.00

*b. 1.33

c. 2.08

d. 4.08

e. 0.7562. If X ~ U(11, 16), what is the variance of X?

a. 3.00

b. 1.33

*c. 2.08

d. 4.08


a. 3.00

b. 1.33

c. 2.08

*d. 4.08


a. 3.00

b. 1.33

c. 2.08

d. 4.08

*e. 0.7565. 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 minutes2b. 31.8 minutes

c. 65 minutes2d. 100 minutes2e. 25 minutes

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 minutes2*b. 31.8 minutes

c. 65 minutes2d. 100 minutes2e. 25 minutes

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

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

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. 0.082b. 0.024

c. 0.287

d. 0.135

e. 0.368

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


b. 0.024

*c. 0.287

d. 0.135

e. 0.368


b. 0.024

c. 0.287

*d. 0.135

e. 0.368


b. 0.024

c. 0.287

d. 0.135

*e. 0.368

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


a. 0.557

*b. 0.524

c. 0.471

d. 0.233

e. 0.204


a. 0.557

b. 0.524

*c. 0.471

d. 0.233

e. 0.204


a. 0.557

b. 0.524

c. 0.471

*d. 0.233

e. 0.204


a. 0.557

b. 0.524

c. 0.471

d. 0.233

*e. 0.204

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. 0.189c. 0.368d. 0.097e. 0.01880. 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. 0.189c. 0.368d. 0.097e. 0.01881. 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 3 minutes before the first customer arrives for the day after the bank has opened at 8am?

a. 0.036

b. 0.189*c. 0.368d. 0.097e. 0.01882. 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 7 minutes before the first customer arrives for the day after the bank has opened at 8am?

a. 0.036

b. 0.189c. 0.368*d. 0.097e. 0.01883. 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 12 minutes before the first customer arrives for the day after the bank has opened at 8am?

a. 0.036

b. 0.189c. 0.368d. 0.097*e. 0.01884. The time it takes a technician to fix a computer is exponentially distributed with a mean of 15 minutes. What is the probability that it will take the technician less than 10 minutes to fix a randomly selected computer?

*a. 0.487b. 0.373

c. 0.632

d. 0.393

e. 0.551

85. The time it takes a technician to fix a computer is exponentially distributed with a mean of 15 minutes. What is the probability that it will take the technician less than 7 minutes to fix a randomly selected computer?

a. 0.487

*b. 0.373

c. 0.632

d. 0.393

e. 0.551


a. 0.487

b. 0.373

*c. 0.632

d. 0.393

e. 0.551


a. 0.487

b. 0.373

c. 0.632

*d. 0.393

e. 0.551


a. 0.487

b. 0.373

c. 0.632

d. 0.393

*e. 0.551

89. Flaws occur in telephone cabling at an average rate of 4.4 flaws per 1km of cable. What is the probability that the distance between two flaws exceeds 0.5km?

*a. 0.111

b. 0.012

c. 0.001

d. 0.202

e. 0.041

90. Flaws occur in telephone cabling at an average rate of 4.4 flaws per 1km of cable. What is the probability that the distance between two flaws exceeds 1km?

a. 0.111

*b. 0.012

c. 0.001

d. 0.202

e. 0.041


a. 0.111

b. 0.012

*c. 0.001

d. 0.202

e. 0.041


a. 0.111

b. 0.012

c. 0.001

*d. 0.202

e. 0.041

93. Flaws occur in telephone cabling at an average rate of 3.2 flaws per 1km of cable. What is the probability that the distance between two flaws exceeds 1km?

a. 0.111

b. 0.012

c. 0.001

d. 0.202

*e. 0.041

94. Textbooks are sold at a university bookshop at an average rate of 2 per hour. What is the probability that it will be less than 20 minutes before the next textbook is sold?

*a. 0.487b. 0.283

c. 0.632

d. 0.528

e. 0.393


a. 0.487

*b. 0.283

c. 0.632

d. 0.528

e. 0.393


a. 0.487

b. 0.283

*c. 0.632

d. 0.528

e. 0.393


a. 0.487

b. 0.283

c. 0.632

*d. 0.528

e. 0.393


a. 0.487

b. 0.283

c. 0.632

d. 0.528

*e. 0.393

99. The time it takes a technician to fix a computer is exponentially distributed with a mean of 15 minutes. What is the variance of the amount of time it takes a technician to fix a computer?

*a. 225

b. 15

c. 0.004d. 0.067e. 20

100. The time it takes a technician to fix a computer is exponentially distributed with a mean of 15 minutes. What is the standard deviation of the amount of time it takes a technician to fix a computer?

a. 225

*b. 15

c. 0.004d. 0.067e. 20

101. The time it takes a technician to fix a computer is exponentially distributed with a mean of 10 minutes. What is the variance of the amount of time it takes a technician to fix a computer?

a. 0.01b. 0.1*c. 100

d. 10

e. 20


a. 0.01b. 0.1c. 100

*d. 10

e. 20


a. 0.05b. 15

c. 100

d. 10

*e. 20

104. Flaws occur in telephone cabling at an average rate of 4.4 flaws per 1km of cable. What is the expected distance between flaws (in km)?

a. 4.4

b. 3.2

*c. 0.227

d. 0.313

e. 2.2

105. Flaws occur in telephone cabling at an average rate of 3.2 flaws per 1km of cable. What is the expected distance between flaws (in km)?

a. 4.4

b. 3.2

c. 0.227

*d. 0.313

e. 2.2

106. Flaws occur in telephone cabling at an average rate of 4.4 flaws per 1km of cable. What is the variance of the distance between flaws?

*a. 0.052b. 0.098c. 19.36d. 10.24

e. 2.2

107. Flaws occur in telephone cabling at an average rate of 3.2 flaws per 1km of cable. What is the variance of the distance between flaws?

a. 0.052*b. 0.098c. 19.36d. 10.24e. 2.2

108. Cars arrive at a tollgate at an average rate of 10 cars per hour. What is the mean time between arrivals (in minutes)?

*a. 6 minutesb. 0.1 minutes

c. 3 minutes

d. 0.05 minutes

e. 4 minutes


a. 6 minutes

b. 0.1 minutes

*c. 3 minutes

d. 0.05 minutes

e. 4 minutes


a. 6 minutes

b. 0.1 minutes

c. 3 minutes

d. 0.05 minutes

*e. 4 minutes

111. The convenor of a first-year statistics programme at a certain university receives, on average, 5 emails per 30 minutes. What is the mean time between the arrival of emails in her inbox (in minutes)?

a. 30 minutes

b. 0.167 minutes

*c. 6 minutesd. 0.5 minutes

e. 5 minutes

112. The convenor of a first-year statistics programme at a certain university receives, on average, 5 emails per 30 minutes. What is the variance of the time between the arrival of emails in her inbox?

a. 36 minutes

*b. 36 minutes2c. 6 minutes

d. 6 minutes2

e. 0.028 minutes2113. Calls are received by the switchboard of a large company at an average rate of 10 calls every 15 minutes. What is the mean time between calls (in minutes)?a. 2 minutes

b. 0.67 minutes

c. 15 minutes

d. 10 minutes

*e. 1.5 minutes114. You and I own a company called Deliveries Inc. We have a large fleet of delivery trucks. On average we have 10 breakdowns per 5 day working week. What is the expected time (in days) between breakdowns?

a. 1 day

*b. 0.5 dayc. 2 days

d. 0.75 daye. 5 days115. You own a very old car which breaks down, on average, 3 times a year. What is the mean time between break downs, in months, of your car?

a. 3 months

b. 0.25 months

c. 12 months

*d. 4 months

e. 0.5 months

116. You own a very old car which breaks down, on average, 3 times a year. What is the standard deviation of the time between break downs, in months, of your car?

a. 3 months

b. 0.25 months

c. 12 months

*d. 4 months

e. 0.5 months

117. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. What proportion of oranges in the orchard have a diameter between 110mm and 130mm?

*a. 0.6826

b. 0.8186

c. 0.3829

d. 0.4332

e. 0.2858


a. 0.6826

*b. 0.8186

c. 0.3829

d. 0.4332

e. 0.2858


a. 0.6826

b. 0.8186

*c. 0.3829

d. 0.4332

e. 0.2858


a. 0.6826

b. 0.8186

c. 0.3829

*d. 0.4332

e. 0.2858


a. 0.6826

b. 0.8186

c. 0.3829

d. 0.4332

*e. 0.2858

122. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is within one standard deviation of the mean?

*a. 0.683b. 0.954

c. 0.271

d. 0.340

e. 0.161

123. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 50 and 90?

a. 0.683

*b. 0.954

c. 0.271

d. 0.340

e. 0.161


a. 0.683

b. 0.954

*c. 0.271

d. 0.340

e. 0.161


a. 0.683

b. 0.954

c. 0.271

*d. 0.340

e. 0.161

126. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 50 and 61?a. 0.683

b. 0.954

c. 0.271

d. 0.340

*e. 0.161

127. The starting annual salaries of newly qualified chartered accountants (CAs) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the probability that a randomly selected newly qualified CA will earn between R160,000 and R190,000 per annum?

*a. 0.819b. 0.242

c. 0.286

d. 0.533

e. 0.307


a. 0.819

*b. 0.242

c. 0.286

d. 0.533

e. 0.307


a. 0.819

b. 0.242

*c. 0.286

d. 0.533

e. 0.307


a. 0.819

b. 0.242

c. 0.286

*d. 0.533

e. 0.307


a. 0.819

b. 0.242

c. 0.286

d. 0.533

*e. 0.307

132. Given that X is Normally distributed with a mean of 80 and a variance of 100, what is p(85 < X < 90)?

*a. 0.150

b. 0.341

c. 0.286

d. 0.625

e. 0.533


a. 0.150

*b. 0.341

c. 0.286

d. 0.625

e. 0.533


a. 0.150

b. 0.341

*c. 0.286

d. 0.625

e. 0.533


a. 0.150

b. 0.341

c. 0.286

*d. 0.625

e. 0.533


a. 0.150

b. 0.341

c. 0.286

d. 0.625

*e. 0.533

137. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm2. What proportion of students are between 162cm and 182cm in height?

*a. 0.954

b. 0.601

c. 0.718

d. 0.883

e. 0.270


a. 0.954

*b. 0.601

c. 0.718

d. 0.883

e. 0.270


a. 0.954

b. 0.601

*c. 0.718

d. 0.883

e. 0.270


a. 0.954

b. 0.601

c. 0.718

*d. 0.883

e. 0.270


a. 0.954

b. 0.601

c. 0.718

d. 0.883

*e. 0.270

142. A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls last less than 180 seconds or more than 300 seconds?

a. 0.911

b. 0.034*c. 0.134

d. 0.067

e. 0.548

143. A bakery finds that the average weight of its most popular package of cookies is 32.06g with a standard deviation of 0.10g. Assuming that the weight of the package of cookies follows a normal distribution, what portion of cookie packages will weigh less than 31.90 g or more than 32.30 g?

*a. 0.06

b. 0.24

c. 0.78

d. 0.01

e. 0.00

144. A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?

a. 0.214

b. 0.094

c. 0933

d. 0.466

*e. 0.067

145. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm2. What is the probability that a randomly selected student from this class will be taller than 180cm?

*a. 0.055b. 0.655

c. 0.274

d. 0.919

e. 0.992


a. 0.055

*b. 0.655

c. 0.274

d. 0.919

e. 0.992


a. 0.055

b. 0.655

*c. 0.274

d. 0.919

e. 0.992


a. 0.055

b. 0.655

c. 0.274

*d. 0.919

e. 0.992


a. 0.055

b. 0.655

c. 0.274

d. 0.919

*e. 0.992

150. Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = -1.75 is:

a. 0.4854

b. 0.4599

c. 0.0146

d. 0.0401

*e. 0.0547

151. The time until first failure of a brand of inkjet printers is normally distributed with a mean of 1500 hours and a standard deviation of 200 hours. What proportion of printers fails before 1000 hours?

*a. 0.0062

b. 0.0668

c. 0.8413

d. 0.0228

e. 0.6915


a. 0.0062

*b. 0.0668

c. 0.8413

d. 0.0228

e. 0.6915


a. 0.0062

b. 0.0668

*c. 0.8413

d. 0.0228

e. 0.6915


a. 0.0062

b. 0.0668

c. 0.8413

*d. 0.0228

e. 0.6915


a. 0.0062

b. 0.0668

c. 0.8413

d. 0.0228

*e. 0.6915

156. Student marks for a first-year Statistics class test follow a normal distribution with a mean of 63% and a standard deviation of 7%. What is the probability that a randomly selected student who wrote the test got more than 75%?

*a. 0.043

b. 0.388

c. 0.159

d. 0.666

e. 0.968


a. 0.043

*b. 0.388

c. 0.159

d. 0.666

e. 0.968


a. 0.043

b. 0.388

*c. 0.159

d. 0.666

e. 0.968


a. 0.043

b. 0.388

c. 0.159

*d. 0.666

e. 0.968


a. 0.043

b. 0.388

c. 0.159

d. 0.666

*e. 0.968

161. The weights of newborn human babies are normally distributed with a mean of 3.2kg and a standard deviation of 1.1kg. What is the probability that a randomly selected newborn baby weighs less than 2.0kg?

*a. 0.138b. 0.428

c. 0.766

d. 0.262

e. 0.607


a. 0.138

*b. 0.428

c. 0.766

d. 0.262

e. 0.607


a. 0.138

b. 0.428

*c. 0.766

d. 0.262

e. 0.607


a. 0.138

b. 0.428

c. 0.766

*d. 0.262

e. 0.607


a. 0.138

b. 0.428

c. 0.766

d. 0.262

*e. 0.607

166. Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of R1,295.00 and a standard deviation of R750.00. What proportion of credit card holders spend more than R1,500.00 on their credit cards per month?

a. 0.487

*b. 0.392

c. 0.500

d. 0.791

e. 0.608

167. Let z be a standard normal value that is unknown but identifiable by position and area. If the area to the right of z is 0.8413, then the value of z must be:

a. 1.00

*b. -1.00

c. 0.00

d. 0.41

e. -0.41

168. Let z be a standard normal value that is unknown but identifiable by position and area. If the symmetrical area between negative z and positive z is 0.9544 then the value of z must be:

*a. 2.00

b. 0.11

c. 2.50

d. 0.06

e. 2.20

169. If the area to the right of a positive value of z (z has a standard normal distribution) is 0.0869 then the value of z must be:

a. 0.22

b. -1.36

*c. 1.36

d. 1.71

e. -1.71

170. If the area between 0 and a positive value of z (z has a standard normal distribution) is 0.4591 then the value of z is:*a. 1.74

b. -1.74

c. 0.18

d. -0.18

e. 1.84

171. If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?*a. -1.41

b. 1.41

c. -2.25

d. 2.25

e. -0.03

172. If the area to the left of a value of z (z has a standard normal distribution) is 0.0122, what is the value of z?

a. -1.41

b. 1.41

*c. -2.25

d. 2.25

e. -0.03


*a. -0.89

b. 0.89

c. -1.02

d. 1.02

e. -2.37


a. -0.89

b. 0.89

*c. -1.02

d. 1.02

e. -2.37


a. -0.89

b. 0.89

c. -1.02

d. 1.02

*e. -2.37

176. If the area to the right of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?

a. -1.41

*b. 1.41

c. -2.25

d. 2.25

e. -0.03


a. -1.41

b. 1.41

c. -2.25

*d. 2.25

e. -0.03


a. -0.89

*b. 0.89

c. -1.02

d. 1.02

e. -2.37


a. -0.89

b. 0.89

c. -1.02

*d. 1.02

e. -2.37


a. -0.89

b. 0.89

c. -1.02

d. 1.02

*e. 2.37

181. If P(Z > z) = 0.6844 what is the value of z (z has a standard normal distribution)?

*a. -0.48

b. 0.48

c. -1.04

d. 1.04

e. -0.21

182. If P(Z < z) = 0.6844 what is the value of z (z has a standard normal distribution)?

a. -0.48

*b. 0.48

c. -1.04

d. 1.04

e. -0.21


a. -0.48

b. 0.48

*c. -1.04

d. 1.04

e. -0.21


a. -0.48

b. 0.48

c. -1.04

*d. 1.04

e. -0.21


a. -0.48

b. 0.48

c. -1.04

d. 1.04

*e. -0.21


a. -0.48

b. 0.48

c. -1.04

d. 1.04

*e. 0.21


*a. -2.12

b. 2.12

c. -1.77

d. 1.77

e. -0.21


a. -2.12

*b. 2.12

c. -1.77

d. 1.77

e. -0.21


a. -2.12

b. 2.12

*c. -1.77

d. 1.77

e. -0.21


a. -2.12

b. 2.12

c. -1.77

*d. 1.77

e. -0.21

191. Given that z is a standard normal random variable and that the area to the left of z is 0.305, then the value of z is:

a. 0.51

*b. -0.51

c. 0.86

d. -0.86

e. 0.24

192. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The smallest 10% of oranges (those with the smallest diameters) cannot be sold and are therefore given away. What is the cut-off diameter in this case if oranges with the smallest 10% of diameters are to be given away?

*a. 107.2

b. 103.6c. 111.6

d. 109.6

e. 105.9


a. 107.2

*b. 103.6

c. 111.6

d. 109.6

e. 105.9


a. 107.2

b. 103.6

*c. 111.6

d. 109.6

e. 105.9


a. 107.2

b. 103.6

c. 111.6

*d. 109.6

e. 105.9


a. 107.2

b. 103.6

c. 111.6

d. 109.6

*e. 105.9

197. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The farmer would like to select the largest 10% of oranges (those with the largest diameters) in order to be able to keep them for himself and his family to enjoy! What is the cut-off diameter in this case if oranges with the largest 10% of diameters are to be kept?

*a. 132.8

b. 136.4

c. 128.4

d. 130.4

e. 134.1


a. 132.8

*b. 136.4

c. 128.4

d. 130.4

e. 134.1


a. 132.8

b. 136.4

*c. 128.4

d. 130.4

e. 134.1


a. 132.8

b. 136.4

c. 128.4

*d. 130.4

e. 134.1


a. 132.8

b. 136.4

c. 128.4

d. 130.4

*e. 134.1

202. The time until first failure of a brand of inkjet printers is normally distributed with a mean of 1500 hours and a standard deviation of 200 hours. Printers are to be sold with a guarantee. The manufacturer of the printers wants only 5% of printers to fail before the guarantee period is up. What number of hours should the guarantee period be set at so that only 5% of printers fail before this time?

*a. 1171 hours

b. 1244 hoursc. 1205 hours

d. 1124 hours

e. 1089 hours


a. 1171 hours

*b. 1244 hours

c. 1205 hours

d. 1124 hours

e. 1089 hours


a. 1171 hours

b. 1244 hours

*c. 1205 hours

d. 1124 hours

e. 1089 hours


a. 1171 hours

b. 1244 hours

c. 1205 hours

*d. 1124 hours

e. 1089 hours


a. 1171 hours

b. 1244 hours

c. 1205 hours

d. 1124 hours

*e. 1089 hours

207. The starting annual salaries of newly qualified chartered accountants (CAs) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the minimum annual salary earned by the top 5% of newly qualified CAs?

*a. R196,449

b. R192,816

c. R190,364

d. R198,808

e. R203,263


a. R196,449

*b. R192,816

c. R190,364

d. R198,808

e. R203,263


a. R196,449

b. R192,816

*c. R190,364

d. R198,808

e. R203,263


a. R196,449

b. R192,816

c. R190,364

*d. R198,808

e. R203,263


a. R196,449

b. R192,816

c. R190,364

d. R198,808

*e. R203,263

212. The starting annual salaries of newly qualified chartered accountants (CAs) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the maximum annual salary earned by the 5% of newly qualified CAs with the lowest salaries?*a. R163,551

b. R167,184

c. R169,636

d. R161,192

e. R156,737

213. The starting annual salaries of newly qualified chartered accountants (CAs) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the maximum annual salary earned by the 10% of newly qualified CAs with the lowest salaries?a. R163,551

*b. R167,184

c. R169,636

d. R161,192

e. R156,737


b. R167,184

*c. R169,636

d. R161,192

e. R156,737


b. R167,184

c. R169,636

*d. R161,192

e. R156,737


b. R167,184

c. R169,636

d. R161,192

*e. R156,737

217. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm2. If only the shortest 10% of students are to be selected to perform a specific task, what is the cut-off height?

a. 178.4cm

b. 123.5cm

*c. 165.6cm

d. 145.7cm

e. 159.2cm

218. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm2. If only the tallest 10% of students are to be selected to perform a specific task, what is the cut-off height?

*a. 178.4cm

b. 123.5cm

c. 165.6cm

d. 145.7cm

e. 159.2cm

219. A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What is the length of a particular call (in seconds) if only 1% of calls are shorter?

*a. 146.95b. 157.85

c. 174.21

d. 333.05

e. 305.79


a. 146.95

*b. 157.85

c. 174.21

d. 333.05

e. 305.79


a. 146.95

b. 157.85

*c. 174.21

d. 333.05

e. 305.79

222. A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What is the length of a particular call (in seconds) if only 1% of calls are longer?

a. 146.95

b. 157.85

c. 174.21

*d. 333.05

e. 305.79

223. A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What is the length of a particular call (in seconds) if only 5% of calls are longer?

a. 146.95

b. 157.85

c. 174.21

d. 333.05

*e. 305.79

224. If X ~ N(, 25) and p(X > 12) = 0.3446. What is the value of ?

*a. 10.00

b. 5.90

c. 1.80

d. 8.05

e. 4.65


a. 10.00

*b. 5.90

c. 1.80

d. 8.05

e. 4.65


a. 10.00

b. 5.90

*c. 1.80

d. 8.05

e. 4.65


a. 10.00

b. 5.90

c. 1.80

*d. 8.05

e. 4.65


a. 10.00

b. 5.90

c. 1.80

d. 8.05

*e. 4.65

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Quiz 5 Continuous Distributions