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Continuous Distributions True/False & Multiple Choice
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Continuous Distributions

True/False

1. A uniform continuous distribution is also referred to as a rectangular distribution.

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Easy

2. The height of the rectangle depicting a uniform distribution is the probability of each outcome and it same for all of the possible outcomes

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

3. The area of the rectangle depicting a uniform distribution        is always equal to one.

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

4. Many human characteristics such as height and weight and many measurements such as variables such as household insurance and cost per square foot of rental space are normally distributed.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

5. Normal distribution is a skewed distribution with its tails extending to infinity on either side of the mean.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

6. Since a normal distribution curve extends from minus infinity to plus infinity, the area under the curve is infinity.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

7. A z-score is the number of standard deviations that a value of a random variable is above or below the mean.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

8. A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

9. A standard normal distribution has a mean of zero and a standard deviation of one.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

10. The standard normal distribution is also called a finite distribution because its mean is zero and standard deviation one, always.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

11. In a standard normal distribution, if the area under curve to the right of a z-value is 0.10, then the area to the left of the same z-value is -0.10.

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

12. Binomial distributions in which the sample sizes are large may be approximated by a Poisson distribution.

Ans:

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Medium

13. A correction for continuity must be made when approximating the binomial distribution problems using a normal distribution.

Ans:

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Medium

14. If arrivals at a bank followed a Poisson distribution, then the time between arrivals would follow a binomial distribution.

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

15. For an exponential distribution, the mean is always equal to its variance.

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Multiple Choice

16. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then the height of this distribution, f(x), is __________________.

a) 1/8

b) 1/4

c) 1/12

d) 1/20

e)  1/24

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Easy

17. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then the mean of this distribution is __________________.

a) 10

b) 20

c) 5

d) 0

e) unknown

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

18. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then the standard deviation of this distribution is __________________.

a) 4.00

b) 1.33

c) 1.15

d) 2.00

e) 1.00

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

19. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then the probability, P(9  x  11), is __________________.

a) 0.250

b) 0.500

c) 0.333

d) 0.750

e) 1.000

2Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

20. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then the probability, P(10.0  x  11.5), is __________________.

a) 0.250

b) 0.333

c) 0.375

d) 0.500

e) 0.750

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

21. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then the probability, P(13  x  15), is __________________.

a) 0.250

b) 0.500

c) 0.375

d) 0.000

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

22. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then   P(x < 7) is __________________.

a) 0.500

b) 0.000

c) 0.375

d) 0.250

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

23. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then   P(x  11) is __________________.

a) 0.750

b) 0.000

c) 0.333

d) 0.500

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

24. If x is uniformly distributed over the interval 8 to 12, inclusively (8  x  12), then P(x  10) is __________________.

a) 0.750

b) 0.000

c) 0.333

d) 0.500

e) 0.900

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

25. If a continuous random variable x is uniformly distributed over the interval 8 to 12, inclusively, then P(x = exactly 10) is __________________.

a) 0.750

b) 0.000

c) 0.333

d) 0.500

e) 0.900

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Hard

26. If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the height of this distribution, f(x), is __________________.

a) 1/10

b) 1/20

c) 1/30

d) 12/50

e) 1/60

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Easy

27. If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the mean of this distribution is __________________.

a) 50

b) 25

c) 10

d) 15

e) 5

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

28. If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the standard deviation of this distribution is __________________.

a) unknown

b) 8.33

c) 0.833

d) 2.89

e) 1.89

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

29. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the probability that an oil change job is completed in 25 to 28 minutes, inclusively, i.e., P(25  x  28) is __________________.

a) 0.250

b) 0.500

c) 0.300

d) 0.750

e) 81.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

30. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the probability that an oil change job is completed in 21.75 to 24.75 minutes, inclusively, i.e., P(21.75  x  24.25) is __________________.

a) 0.250

b) 0.333

c) 0.375

d) 0.000

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

31. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the probability that an oil change job is completed in 33 to 35 minutes, inclusively, i.e., P(33  x  35) is __________________.

a) 0.5080

b) 0.000

c) 0.375

d) 0.200

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

32. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the probability that an oil change job is completed in less than 17 minutes, i.e., P(x < 17) is __________________.

a) 0.500

b) 0.300

c) 0.000

d) 0.250

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

33. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the probability that an oil change job is completed in less than or equal to 22 minutes, i.e.,  P(x  22) is __________________.

a) 0.200

b) 0.300

c) 0.000

d) 0.250

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

34. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20  x  30), then the probability that an oil change job will be completed 24 minutes or more, i.e., P(x  24) is __________________.

a) 0.100

b) 0.000

c) 0.333

d) 0.600

e) 1.000

Ans:

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

35. The normal distribution is an example of _______.

a) a discrete distribution

b) a continuous distribution

c) a bimodal distribution

d) an exponential distribution

e) a binomial distribution

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

36. The total area underneath any normal curve is equal to _______.

a) the mean

b) one

c) the variance

d) the coefficient of variation

e) the standard deviation

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

37. The area to the left of the mean in any normal distribution is equal to _______.

a) the mean

b) 1

c) the variance

d) 0.5

e) -0.5

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

38. A standard normal distribution has the following characteristics:

a) the mean and the variance are both equal to 1

b) the mean and the variance are both equal to 0

c) the mean is equal to the variance

d) the mean is equal to 0 and the variance is equal to 1

e) the mean is equal to the standard deviation

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

39. If x is a normal random variable with mean 80 and standard deviation 5, the z-score for x = 88 is ________.

a) 1.8

b) -1.8

c) 1.6

d) -1.6

e) 8.0

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

40. Suppose x is a normal random variable with mean 60 and standard deviation 2.  A z score was calculated for a number, and the z score is 3.4.  What is x?

a) 63.4

b) 56.6

c) 68.6

d) 53.2

e) 66.8

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

41. Suppose x is a normal random variable with mean 60 and standard deviation 2.  A z score was calculated for a number, and the z score is -1.3.  What is x?

a) 58.7

b) 61.3

c) 62.6

d) 57.4

e) 54.7

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

42. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z < 1.3)?

a) 0.4032

b) 0.9032

c) 0.0968

d) 0.3485

e) 0. 5485

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

43. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(1.3 < z < 2.3)?

a) 0.4032

b) 0.9032

c) 0.4893

d) 0.0861

e) 0.0086

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

44. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > 2.4)?

a) 0.4918

b) 0.9918

c) 0.0082

d) 0.4793

e) 0.0820

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

45. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z < -2.1)?

a) 0.4821

b) -0.4821

c) 0.9821

d) 0.0179

e) -0.0179

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

46. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > -1.1)?

a) 0.36432

b) 0.8643

c) 0.1357

d) -0.1357

e) -0.8643

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

47. Let z be a normal random variable with mean 0 and standard deviation 1. What is

P(-2.25 < z < -1.1)?

a) 0.3643

b) 0.8643

c) 0.1235

d) 0.4878

e) 0.5000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

48. Let z be a normal random variable with mean 0 and standard deviation 1. The 50th percentile of z is ____________.

a) 0.6700

b) -1.254

c) 0.0000

d) 1.2800

e) 0.5000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

49. Let z be a normal random variable with mean 0 and standard deviation 1. The 75th percentile of z is ____________.

a) 0.6700

b) -1.254

c) 0.0000

d) 1.2800

e) 0.5000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

50. Let z be a normal random variable with mean 0 and standard deviation 1. The 90th percentile of z is ____________.

a) 1.645

b) -1.254

c) 1.960

d) 1.280

e) 1.650

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

51.          A z score is the number of __________ that a value is from the mean.

a) variances

b) standard deviations

c) units

d) miles

e) minutes

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

52.          Within a range of z scores from -1 to +1, you can expect to find _______ per cent of the values in a normal distribution.

a) 95

b) 99

c) 68

d) 34

e) 100

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

53.          Within a range of z scores from -2 to +2, you can expect to find _______ per cent of the values in a normal distribution.

a) 95

b) 99

c) 68

d) 34

e) 100

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Easy

54.          The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.  The life of this bulb is normally distributed.  What is the probability that a randomly selected bulb would last longer than 1150 hours?

a) 0.4987

b) 0.9987

c) 0.0013

d) 0.5013

e) 0.5513

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

55.          The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 1100 hours?

a) 0.4772

b) 0.9772

c) 0.0228

d) 0.5228

e) 0.5513

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

56.          The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed.  What is the probability that a randomly selected bulb would last fewer than 940 hours?

a) 0.3849

b) 0.8849

c) 0.1151

d) 0.6151

e) 0.6563

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Medium

57.          Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20.  Determine the value of x such that 60% of the values are greater than x.

a) 404.5

b) 395.5

c) 405.0

d) 395.0

e) 415.0

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

58.          Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life of at most 30,000 miles?

a) 0.5000

b) 0.4772

c) 0.0228

d) 0.9772

e) 1.0000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

59.          Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life of at least 50,000 miles?

a) 0.0228

b) 0.9772

c) 0.5000

d) 0.4772

e) 1.0000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

60.          Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles?

a) 0.5000

b) 0.4772

c) 0.9544

d) 0.9772

e) 1.0000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

61.          The net profit from a certain investment is normally distributed with a mean of \$10,000 and a standard deviation of \$5,000. The probability that the investor will not have a net loss is _____________.

a) 0.4772

b) 0.0228

c) 0.9544

d) 0.9772

e) 1.0000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

62.          The net profit of an investment is normally distributed with a mean of \$10,000 and a standard deviation of \$5,000.  The probability that the investor’s net gain will be at least \$5,000 is _____________.

a) 0.1859

b) 0.3413

c) 0.8413

d) 0.4967

e) 0.5000

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

63.          Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days.  The probability that the project will be completed within 185 work-days is ______.

a) 0.0668

b) 0.4332

c) 0.5000

d) 0.9332

e) 0.9950

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

64.          Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days. To be 99% sure that we will not be late in completing the project, we should request a completion time of _______ work-days.

a) 211

b) 207

c) 223

d) 200

e) 250

Ans:

Response: See section 6.2, Normal Distribution

Difficulty: Hard

65.          Let x be a binomial random variable with n=20 and p=.8.  If we use the normal distribution to approximate probabilities for this, we would use a mean of _______.

a) 20

b) 16

c) 3.2

d) 8

e) 5

Ans:

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Easy

66.          Let x be a binomial random variable with n=20 and p=.8.  If we use the normal distribution to approximate probabilities for this, a correction for continuity should be made. To find the probability of more than 12 successes, we should find _______.

a) P(x>12.5)

b) P(x>12)

c) P(x>11.5)

d) P(x<11.5)

e) P(x < 12)

Ans:

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Medium

67.          The exponential distribution is an example of _______.

a) a discrete distribution

b) a continuous distribution

c) a bimodal distribution

d) a normal distribution

e) a symmetrical distribution

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Easy

68.          For an exponential distribution with a lambda () equal to 4, the standard deviation equal to _______.

a) 4

b) 0.5

c) 0.25

d) 1

e) 16

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Medium

69.          The average time between phone calls arriving at a call center is 30 seconds. Assuming that the time between calls is exponentially distributed, find the probability that more than a minute elapses between calls.

a) 0.135

b) 0.368

c) 0.865

d) 0.607

e) 0.709

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

70.          The average time between phone calls arriving at a call center is 30 seconds.  Assuming that the time between calls is exponentially distributed, find the probability that less than two minutes elapse between calls.

a) 0.018

b) 0.064

c) 0.936

d) 0.982

e) 1.000

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

71.          At a certain workstation in an assembly line, the time required to assemble a component is exponentially distributed with a mean time of 10 minutes. Find the probability that a component is assembled in 7 minutes or less?

a) 0.349

b) 0.591

c) 0.286

d) 0.714

e) 0.503

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

72.          At a certain workstation in an assembly line, the time required to assemble a component is exponentially distributed with a mean time of 10 minutes. Find the probability that a component is assembled in 3 to 7 minutes?

a) 0.5034

b) 0.2592

c) 0.2442

d) 0.2942

e) 0.5084

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

73.          On Saturdays, cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The probability that at least 2 minutes will elapse between car arrivals is _____________.

a) 0.0000

b) 0.4493

c) 0.1353

d) 1.0000

e) 1.0225

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

74.          On Saturdays, cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The probability that less than 10 minutes will elapse between car arrivals is _____________.

a) 0.8465

b) 0.9817

c) 0.0183

d) 0.1535

e) 0.2125

Ans:

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

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