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Continuous Distributions True/False & Multiple Choice
Ch06: Chapter 6, 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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FalseResponse: *** ******* ** *********** DistributionDifficulty: ****************** ************** ** * is ********* *********** **** *** interval * to ** *********** (8 ** x £ *** then *** ****** ** this ************ **** ** __________________a) 1/8b) ***** ****** ****** ********** ********** See section ** The ******* *********************** Easy 17 If * is ********* *********** over *** ******** * to ** *********** ** ** * ** 12) **** *** **** ** this distribution is ******************** **** **** *** *** ************* ********** *** ******* ** The ******* DistributionDifficulty: ************** ** x ** ********* *********** **** *** ******** * to ** *********** ** ** * ** *** **** the ******** ********* ** this ************ ** ******************** ***** ***** 115d) ***** ********* ********** See ******* ** The ******* *********************** Medium 19 ** x ** ********* *********** **** the ******** * ** 12 *********** ** £ * ** *** **** *** *********** *** £ * £ *** ** __________________a) ****** ****** ****** ****** *********** ********** *** ******* ** The Uniform DistributionDifficulty: ************** ** * is uniformly *********** **** the ******** 8 to 12 *********** (8 ** * £ 12) **** the probability ***** ** * £ **** ** ******************** 0250b) 0333c) ****** 0500e) ********** ********** *** ******* 61 *** ******* *********************** Medium 21 ** x ** ********* *********** over the ******** * ** 12 inclusively ** ** x ** *** **** the *********** **** ** x ** *** ** ******************** ****** 0500c) ****** 0000e) ********** ********** *** section ** *** ******* DistributionDifficulty: Medium 22 ** x ** uniformly *********** **** *** ******** * ** ** inclusively ** £ * ** *** then *** < ** ** ******************** ****** 0000c) 0375d) ****** ********** ********** See section ** The ******* *********************** Medium 23 ** * is ********* *********** over the ******** * ** ** *********** ** ** * £ *** **** *** ** *** is __________________a) ****** ****** ****** ****** 1000 Ans: ********** See ******* 61 The ******* *********************** ************** ** * is uniformly *********** over *** ******** 8 ** 12 *********** ** £ * £ *** **** P(x ³ *** ** ********************** ****** ****** ****** ****** ********** dResponse: *** section 61 *** ******* *********************** Medium 25 ** * continuous random ******** * ** ********* *********** over *** interval * to 12 *********** then *** * exactly 10) ** __________________ a) ****** 0000c) ****** 0500e) ********** bResponse: *** section 61 *** Uniform *********************** ************ ** * *** **** *** ******** to ******** ** oil ****** *** ** ******* **** service ******* ** ********* *********** **** *** interval 20 ** 30 *********** *** ** * £ *** **** the ****** ** this distribution **** ** ******************** ****** ****** ****** 12/50e) 1/60 Ans: ********** See ******* ** *** ******* *********************** Easy 27 ** * *** **** *** ******** ** ******** ** *** change *** ** certain auto ******* ******* ** ********* distributed **** *** ******** ** ** ** inclusively (20 ** * £ *** **** *** **** of **** ************ ** ******************** 50b) 25c) **** 15e) ******* ********** See ******* ** The ******* *********************** ************** If x *** **** *** minutes) ** ******** ** *** ****** *** ** ******* **** ******* station is ********* *********** **** the ******** 20 to ** *********** *** £ * ** *** **** *** ******** ********* ** **** ************ ** ******************** ********* 833c) 0833d) 289e) ********* ********** *** ******* ** The Uniform DistributionDifficulty: Medium 29 ** x *** time *** ******** to ******** ** ****** job ** ******* **** ******* ******* ** ********* distributed over *** ******** ** ** ** *********** *** ** * ** *** then the *********** **** ** oil change job is completed ** ** ** 28 ******* *********** ** **** £ * ** *** ** ******************** ****** 0500c) ****** ****** 81000 Ans: ********** See ******* ** The Uniform DistributionDifficulty: ************** ** x the **** *** ******** to complete ** change *** ** ******* **** ******* station ** ********* *********** **** *** ******** ** ** 30 inclusively (20 £ * £ *** **** the *********** **** ** *** ****** *** ** ********* ** 2175 ** **** ******* *********** ** ****** ** x £ ***** ** ******************** 0250b) ****** ****** ****** 1000 Ans: ********** *** ******* ** *** Uniform *********************** ************** ** x *** **** *** minutes) to complete ** ****** job ** ******* auto ******* ******* is ********* *********** **** *** ******** ** ** ** *********** *** ** * ** 30) **** *** *********** **** an *** change *** ** ********* ** ** to 35 minutes *********** ** **** ** x ** 35) is ******************** ******* ****** ****** ****** ********** ********** *** ******* ** *** Uniform *********************** ************** ** * *** **** *** ******** ** ******** ** ****** job ** certain **** ******* station ** uniformly *********** **** *** ******** ** to ** *********** (20 ** * £ 30) **** the *********** **** ** *** ****** *** is ********* in **** than ** minutes ** P(x **** 17) ** ******************** ****** 0300c) ****** 0250e) 1000 Ans: ********** *** section ** *** ******* *********************** ************** ** * *** time (in minutes) ** complete ** change job at ******* **** service ******* ** uniformly *********** over *** ******** 20 ** 30 *********** *** ** * ** *** then *** probability **** an oil ****** *** ** completed ** **** **** or ***** to ** ******* ** *** ** *** ** __________________a) ****** ****** 0000d) ****** ********** ********** *** ******* 61 *** ******* *********************** ************** If * *** time *** minutes) ** ******** ** ****** *** ** ******* **** service ******* is uniformly distributed **** *** ******** ** ** ** *********** *** ** * ** *** **** *** *********** **** ** oil ****** *** **** ** completed ** ******* ** more ie *** ³ *** ** ******************** ****** 0000c) ****** 0600e) ********** ********** *** ******* ** *** ******* DistributionDifficulty: Medium 35 The ****** ************ ** ** example ** ********* * ******** ************** a ********** distributionc) * bimodal distributiond) ** *********** ************** a ******** ****************** ********** See section 62 ****** DistributionDifficulty: ************ The total area underneath any ****** curve ** ***** ** ********* *** meanb) ***** the ********** *** *********** ** variatione) *** standard *************** ********** See ******* 62 Normal *********************** ************ *** **** ** the left ** the mean in *** normal ************ ** equal to _______a) the ****** 1c) the ********** 05e) ********* dResponse: *** section ** Normal DistributionDifficulty: ************ * ******** normal ************ *** *** ********* ****************** *** **** *** the ******** *** both equal ** *** *** mean and the ******** are both ***** ** *** *** **** ** equal ** the varianced) the **** is ***** ** and *** ******** ** equal to 1e) *** **** ** ***** to *** ******** deviation Ans: ********** See ******* 62 ****** *********************** ************** ** x is * ****** random ******** **** **** 80 *** ******** ********* 5 *** ******* *** * * ** is ________a) 18b) ***** **** ***** ******** ********** *** ******* 62 Normal *********************** Medium 40 ******* x ** * normal random ******** **** **** 60 *** ******** ********* * A * score *** ********** *** * number *** *** z ***** ** 34 **** ** x?a) ***** ***** 686d) ***** ********* ********** *** ******* ** Normal *********************** ************** ******* * ** a ****** random ******** with mean ** *** standard deviation 2 * * ***** *** ********** *** * number *** *** * ***** ** *** **** is **** ***** ***** 626d) ***** 547 Ans: ********** *** section ** Normal *********************** ************** *** * ** a ****** random ******** **** mean *** ******** deviation 1 **** ** *** **** ****** 04032b) 09032c) 00968d) ******* 5485 Ans: ********** See ******* ** ****** *********************** ************** *** * ** a ****** random ******** **** **** *** standard ********* * What ** **** **** * **** 23)?a) ******* ******* 04893d) ******* *********** ********** See section 62 ****** *********************** Medium 44 *** * ** * ****** ****** variable **** mean *** standard ********* * **** ** *** **** ****** 04918b) ******* 00082d) 04793e) 00820 Ans: ********** *** section ** Normal *********************** Easy 45 *** * be * normal ****** ******** **** **** *** ******** deviation * **** is *** **** ******* ******* -04821c) ******* ******* ************ ********** *** ******* ** ****** *********************** Medium 46 *** * ** a ****** ****** ******** with mean and ******** ********* * **** ** *** **** ******* ******** ******* ******* ******** ************ bResponse: *** ******* ** ****** DistributionDifficulty: Medium 47 *** * be * ****** ****** ******** **** **** *** ******** ********* * What isP(-225 **** * **** ******* 03643b) ******* ******* 04878e) *********** cResponse: *** section ** Normal *********************** ************** Let * ** a normal ****** variable **** **** and ******** ********* 1 The 50th percentile ** * is ____________a) ******* ******* ******* ******* *********** ********** *** section ** ****** *********************** ************ *** z ** * ****** random ******** **** mean *** ******** ********* 1 *** **** percentile of z ** ************** ******* ******* ******* 12800e) 05000 Ans: ********** *** ******* ** ****** *********************** ************** Let * ** a normal ****** ******** **** **** and ******** ********* * *** **** ********** of * ** ************** 1645b) ******* 1960d) ****** ********** ********** See ******* ** ****** *********************** Medium 51 A * score ** *** ****** of __________ **** a ***** ** **** *** ****** *********** ******** ************ ******* ******* minutes Ans: ********** See ******* 62 ****** *********************** ************ ****** * range of z ****** from -1 ** +1 *** *** ****** ** find ******* per cent ** *** ****** in * ****** distributiona) **** 99c) **** 34e) ********* cResponse: *** ******* ** ****** *********************** ************ ****** a range of * ****** **** ** to +2 you can expect ** **** ******* *** **** ** *** ****** ** * ****** distributiona) **** **** **** 34e) ********* ********** *** ******* ** ****** *********************** ************ *** expected ****** life ** * ********** **** of ***** bulb ** 1000 ***** **** * ******** ********* ** ** ***** *** life ** this bulb is ******** distributed **** ** the *********** **** * ******** ******** **** would last ****** than 1150 ******** ******* 09987c) ******* 05013e) *********** ********** *** section ** Normal *********************** ************** *** ******** (mean) **** ** a ********** type of light **** ** 1000 ***** **** * ******** ********* of 50 ***** *** life ** this bulb ** ******** *********** **** ** *** *********** that * ******** ******** bulb ***** last ***** **** **** ******** ******* ******* 00228d) ******* *********** ********** *** ******* ** ****** *********************** Medium 56 The ******** ****** life ** a ********** **** ** ***** bulb ** **** hours with a ******** ********* of ** ***** *** life ** **** bulb ** ******** distributed What is *** *********** **** * ******** ******** bulb ***** last ***** **** *** ******** ******* ******* 01151d) ******* *********** ********** *** ******* 62 ****** DistributionDifficulty: Medium 57 ******* you are working with a data *** that is ******** *********** **** * **** ** *** *** * ******** ********* ** ** ********* *** value ** x **** **** *** ** *** ****** are ******* **** *** 4045b) ****** 4050d) 3950e) ********** ********** *** section ** ****** *********************** ************ Sure Stone **** Company has *********** that the ****** **** of * ********** ***** ** *** ********** tires ** normally *********** **** * **** ** ***** ***** *** * standard deviation ** **** ***** **** is the *********** that * randomly ******** **** ** **** brand *** * life ** ** **** ***** miles?a) ******* ******* 00228d) 09772e) *********** ********** See ******* ** Normal DistributionDifficulty: ************ Sure ***** **** Company *** established **** the ****** **** ** * ********** ***** ** *** automobile ***** is normally *********** **** * **** of ***** ***** *** * ******** ********* ** **** ***** **** ** *** *********** **** * ******** selected tire of this ***** *** * **** of ** ***** 50000 ******** 00228b) 09772c) 05000d) ******* 10000 Ans: ********** See section 62 ****** DistributionDifficulty: ************ **** Stone **** ******* *** *********** **** the ****** **** of a particular ***** of *** ********** tires ** ******** distributed **** * **** ** 40000 miles *** * ******** ********* ** **** miles What ** *** *********** **** * randomly ******** tire ** **** brand *** * **** between ***** *** ***** ******** ******* ******* ******* 09772e) 10000 Ans: ********** See ******* ** ****** DistributionDifficulty: Hard 61 *** *** ****** from a ******* ********** ** normally *********** **** * **** ** $10000 and a ******** deviation of ***** *** *********** **** *** ******** will not **** * *** **** ** *************** 04772b) 00228c) 09544d) ******* 10000 Ans: dResponse: *** ******* 62 ****** *********************** Hard 62 *** *** ****** ** ** ********** is ******** *********** **** * **** of ****** *** * ******** ********* ** ***** The *********** **** *** ************ *** gain **** ** at ***** ***** ** *************** ******* ******* ******* 04967e) *********** ********** *** ******* 62 ****** *********************** ************ ********** **** ***** ***** ** finish) of * ******** remodeling ******* ** ******** *********** **** a mean ** *** ********* *** * ******** ********* of ** ********* *** probability that *** project **** ** ********* ****** *** ********* is ******** ******* ******* ******* ******* *********** ********** *** section ** Normal *********************** ************ Completion **** ***** start ** ******* ** * building remodeling ******* ** ******** *********** **** * **** of *** ********* *** a ******** deviation of ** ********* ** be *** **** **** ** **** *** ** late ** completing *** ******* we ****** request * completion **** ** ******* *********** ***** ***** ***** ***** ********* ********** *** ******* ** Normal DistributionDifficulty: ************ *** x ** * ******** ****** ******** with **** *** p=8 ** ** use *** ****** ************ to *********** probabilities *** **** ** ***** *** * mean ** _______a) **** **** **** 8e) 5 Ans: bResponse: See section ** Using *** Normal ***** ** *********** ******** ************ ******************* Easy 66 Let x be * ******** ****** variable with **** and p=8 ** we use the ****** distribution ** approximate ************* *** **** * ********** *** continuity ****** ** **** ** **** the *********** ** **** **** ** ********* ** ****** **** ********* ************* P(x>12)c) P(x>115)d) P(x<115)e) *** < 12) Ans: ********** *** ******* ** ***** *** Normal Curve ** Approximate ******** ************ ProblemsDifficulty: ************** *** *********** ************ ** ** example of _______a) * discrete ************** a ********** distributionc) * ******* distributiond) * ****** ************** * symmetrical ****************** ********** *** ******* ** Exponential *********************** ************ *** ** *********** ************ with * lambda *** equal ** 4 *** ******** ********* ***** ** ********* *** **** 025d) *** 16 Ans: ********** *** section 64 *********** DistributionDifficulty: ************** The ******* **** ******* phone ***** arriving at * call ****** is ** seconds Assuming that *** **** ******* ***** ** ************* *********** **** *** probability **** **** **** * ****** ******* between callsa) ****** ****** ****** 0607e) 0709 Ans: ********** *** ******* 64 *********** DistributionDifficulty: ************ *** ******* **** ******* phone calls arriving ** * **** ****** is ** seconds ******** that *** time between calls ** exponentially *********** **** *** probability that **** **** *** ******* ****** ******* callsa) 0018b) ****** ****** ****** ********** ********** See section 64 Exponential *********************** ************ ** * ******* workstation ** ** ******** line *** time ******** to assemble * ********* ** exponentially *********** with a **** **** of ** ******* **** *** *********** that * ********* ** ********* ** 7 ******* ** ******* ****** 0591c) ****** ****** 0503 Ans: ********** *** section ** *********** DistributionDifficulty: ************ ** a ******* workstation in ** ******** **** *** **** ******** ** assemble a ********* ** ************* *********** **** * **** time ** ** minutes **** *** *********** that * component is ********* ** * to 7 ********** ******* 02592c) ******* ******* *********** ********** *** ******* 64 Exponential *********************** Hard 73 On Saturdays **** arrive at *** ********* Scrub *** ***** Car Wash at *** **** ** * cars *** ******* ****** ******** *** *********** that ** ***** * ******* will ****** ******* *** ******** ** *************** ******* ******* ******* ******* *********** ********** *** ******* ** *********** *********************** ************ ** Saturdays cars arrive ** *** ********* ***** and ***** Car **** ** *** **** ** * **** *** ******* ****** ******** *** *********** **** **** than ** ******* **** elapse between *** ******** is *************** 08465b) ******* ******* ******* *********** ********** *** ******* ** Exponential *********************** ************
