ch06

CHAPTER SIX Continuous Distributions D

1. Which of the following is NOT a continuous distribution?

E Term

D E Term

A. B. C. D. 2.

normal distribution exponential distribution uniform distribution binomial distribution

The uniform distribution is _______________. A. B. C. D.

bimodal skewed to the right skewed to the left symmetric

173

174

Test Bank A

3.

E Term

A. B. C. D. 4.

rectangular distribution gamma distribution beta distribution Erlang distribution

The distribution in the following graph is a ________ distribution.

f(X)

D

The uniform distribution is also known as the __________.

0.06 0.05 0.04 0.03 0.02 0.01 0.00 35

E Term

A

E Term

A. B. C. D. 5.

40

45

50

55

60 x 65

normal gamma exponential uniform

The distribution in the following graph is a ________ distribution.

A. B. C. D.

normal gamma exponential uniform

Chapter 6: Continuous Distributions 175 C

6.

E Term

B

A. B. C. D. 7.

E Term

A

8.

M Calc

1/8 1/4 1/12 1/20

If X is uniformly distributed over the interval 8 to 12, inclusively (8  X  12), then the mean() of this distribution is __________________. A. B. C. D.

9.

normal gamma exponential uniform

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. B. C. D.

M Calc

C

The distribution in the following graph is a ________ distribution.

10 20 5 incalculable

If X is uniformly distributed over the interval 8 to 12, inclusively (8  X  12), then the standard deviation () of this distribution is __________________. A. B. C. D.

4 1.33 1.15 2

176

Test Bank B

10.

M Calc

C

A. B. C. D. 11.

M Calc

D

12.

M Calc

A

M Calc

0.250 0.500 0.375 0.000

If X is uniformly distributed over the interval 8 to 12, inclusively (8  X  12), then P(X < 7) is __________________. A. B. C. D.

14.

0.250 0.333 0.375 0.000

If X is uniformly distributed over the interval 8 to 12, inclusively (8  X  12), then the P(13  X  15) is __________________. A. B. C. D.

13.

0.250 0.500 0.333 1.000

If X is uniformly distributed over the interval 8 to 12, inclusively (8  X  12), then the P(10.0  X  11.5) is __________________. A. B. C. D.

M Calc

B

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

0.500 0.000 0.375 0.250

If X is uniformly distributed over the interval 8 to 12, inclusively (8  X  12), then P(X  11) is __________________. A. B. C. D.

0.750 0.000 0.333 0.500

Chapter 6: Continuous Distributions 177 D

15.

E Calc

A

A. B. C. D. 16.

E Calc

B

17.

M Calc

C

M Calc

50 25 10 5

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then the standard deviation () of this distribution is __________________. A. B. C. D.

19.

1/10 1/20 1/30 1/50

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then the mean () of this distribution is __________________. A. B. C. D.

18.

0.750 0.000 0.333 0.500

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then the height of this distribution, f(x), is __________________. A. B. C. D.

M Calc

D

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

incalculable 8.33 0.833 2.89

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then P(25  X  28) is __________________. A. B. C. D.

0.250 0.500 0.300 1.000

178

Test Bank A

20.

M Calc

B

A. B. C. D. 21.

M Calc

C

22.

M Calc

D

M Calc

0.500 0.300 0.000 0.250

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then P(X  22) is __________________. A. B. C. D.

24.

0.500 0.000 0.375 0.200

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then P(X < 17) is __________________. A. B. C. D.

23.

0.250 0.333 0.375 0.000

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then P(33  X  35) is __________________. A. B. C. D.

M Calc

A

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then P(21.75  X  24.25) is __________________.

0.200 0.300 0.000 0.250

If X is uniformly distributed over the interval 20 to 30, inclusively (20  X  30), then P(X  24) is __________________. A. B. C. D.

0.100 0.000 0.333 0.600

Chapter 6: Continuous Distributions 179 C

25.

Helen Casner, a labor relations arbitrator, feels that the amount of time needed to arbitrate a labor dispute is uniformly distributed over the interval 4 to 24 hours, inclusively (4  X  24). Accordingly, the mean (average) time needed to arbitrate a labor dispute is ____________.

M BCalc

A. B. C. D.

D

Helen Casner, a labor relations arbitrator, feels that the amount of time needed to arbitrate a labor dispute is uniformly distributed over the interval 4 to 24 hours, inclusively (4  X  24). Accordingly, the probability that a labor dispute will be arbitrated in 8 hours or less is ____________.

26.

20 hours 16 hours 14 hours 12 hours

M BCalc

A. B. C. D.

C

Helen Casner, a labor relations arbitrator, feels that the amount of time needed to arbitrate a labor dispute is uniformly distributed over the interval 4 to 24 hours, inclusively (4  X  24). Accordingly, the probability that a labor dispute will require between 8 and 16 hours, inclusively, for arbitration is ____________.

27.

0.3333 0.6667 0.0000 0.2000

M BCalc

A. B. C. D.

B

The normal distribution is an example of _______.

28.

E Term

A. B. C. D.

0.3333 0.6667 0.4000 0.2000

a discrete distribution a continuous distribution a bimodal distribution an exponential distribution

180

Test Bank B

29.

The total area underneath any normal curve is _______.

E Term

A. B. C. D.

D

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

30.

equal to the mean equal to 1 equal to the variance equal to the coefficient of variation

E Term

A. B. C. D.

B

For any normal distribution, any value less than the mean would have a _______.

31.

equal to the mean equal to 1 equal to the variance equal to 0.5

E Term

A. B. C. D.

D

A standardized normal distribution has the following characteristics:

32.

positive Z-score negative Z-score negative variance negative probability of occurring

E Term

A. B. C. D.

C

If X is a normal random variable with mean 80 and standard deviation 5, calculate the Z score if X=88.

33.

E Calc

D

E Calc

A. B. C. D. 34.

the mean and variance are both equal to 1 the mean and variance are both equal to 0 the mean is equal to the variance the mean is equal to 0 and the variance is equal to 1

1.8 -1.8 1.6 -1.6

If X is a normal random variable with mean 80 and standard deviation 5, calculate the Z score if X=72. A. B. C. D.

1.8 -1.8 1.6 -1.6

Chapter 6: Continuous Distributions 181 D

35.

E Calc

C

A. B. C. D. 36.

E Calc

C

37.

M Calc

B

E Calc

63.4 56.6 66.8 53.2

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. B. C. D.

39.

1.5 2.5 -1.5 -2.5

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. B. C. D.

38.

2.1 12 1.2 2.4

If X is a normal random variable with mean 60 and standard deviation 2, calculate the Z score if X=57. A. B. C. D.

M Calc

D

If X is a normal random variable with mean 80 and standard deviation 5, calculate the Z score if X=92.

58.7 61.3 62.6 57.4

Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(Z < 1.3). A. B. C. D.

0.4032 0.9032 0.0968 0.3485

182

Test Bank D

40.

E Calc

C

A. B. C. D. 41.

M Calc

D

42.

M Calc

C

M Calc

0.4821 -0.4821 0.9821 0.0179

Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(Z > -1.1). A. B. C. D.

44.

0.4918 0.9918 0.0082 0.4793

Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(Z < -2.1). A. B. C. D.

43.

0.4032 0.9032 0.4893 0.0861

Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(Z > 2.4). A. B. C. D.

M Calc

B

Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(1.3 < Z < 2.3).

0.3643 0.8643 0.1357 -0.1357

Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(-2.25 < Z < -1.1). A. B. C. D.

0.3643 0.8643 0.1235 0.4878

Chapter 6: Continuous Distributions 183 B

45.

M Calc

C

A. B. C. D. 46.

E Calc

A

47.

M Calc

A

M Calc

0.670 -1.254 0.000 1.280

Let Z be a normal random variable with mean 0 and standard deviation 1. The 90th percentile of Z is ____________. A. B. C. D.

49.

0.670 -1.254 0.000 1.280

Let Z be a normal random variable with mean 0 and standard deviation 1. The 75th percentile of Z is ____________. A. B. C. D.

48.

0.3643 0.8521 0.1235 0.4878

Let Z be a normal random variable with mean 0 and standard deviation 1. The 50th percentile of Z is ____________. A. B. C. D.

M Calc

D

Let Z be a normal random variable with mean 0 and standard deviation 1. Use the normal tables to find P(-2.25 < Z < 1.1).

1.645 -1.254 1.960 1.280

Let Z be a normal random variable with mean 0 and standard deviation 1. The 95th percentile of Z is ____________. A. B. C. D.

1.645 -1.254 1.960 1.280

184

Test Bank B

50.

M Calc

C

A. B. C. D. 51.

M Calc

B

52.

M Calc

B

E Calc

0.0987 0.4013 -0.0987 0.5987

Let X be a normal random variable with mean 20 and standard deviation 4. Find P(16 < X < 22). A. B. C. D.

54.

0.2734 0.7734 0.2266 -0.2734

Let X be a normal random variable with mean 20 and standard deviation 4. Find P(X < 19). A. B. C. D.

53.

0.3944 0.8944 0.1056 0.6056

Let X be a normal random variable with mean 20 and standard deviation 4. Find P(X < 17). A. B. C. D.

M Calc

D

Let X be a normal random variable with mean 20 and standard deviation 4. Find P(X < 25).

0.4672 0.0328 0.1498 0.5328

Let X be a normal random variable with mean 20 and standard deviation 4. The 50th percentile of X is ____________. A. B. C. D.

4.000 20.000 22.698 26.579

Chapter 6: Continuous Distributions 185 C

55.

M Calc

A

A. B. C. D. 56.

M Calc

D

57.

M Calc

A

M Calc

25.126 20.000 22.698 26.579

Let X be a normal random variable with mean 40 and standard deviation 8. Find P(32 < X < 44). A. B. C. D.

59.

25.126 20.000 22.698 26.579

Let X be a normal random variable with mean 20 and standard deviation 4. The 95th percentile of X is ____________. A. B. C. D.

58.

25.126 20.000 22.698 26.579

Let X be a normal random variable with mean 20 and standard deviation 4. The 90th percentile of X is ____________. A. B. C. D.

M Calc

D

Let X be a normal random variable with mean 20 and standard deviation 4. The 75th percentile of X is ____________.

0.4672 0.0328 0.1498 0.5328

Let X be a normal random variable with mean 40 and standard deviation 8. Find P(X < 96). A. B. C. D.

1.0000 0.0000 0.0793 0.0575

186

Test Bank B

60.

M Calc

B

Let X be a normal random variable with mean 40 and standard deviation 2. Find P(X < 28). A. B. C. D.

61.

1.0000 0.0000 0.2580 0.0472

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

E Term

A. B. C. D.

C

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

62.

variances standard deviations units miles

E Term

A. B. C. D.

A

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

63.

95 99 68 34

E Term

A. B. C. D.

C

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?

M Calc

64.

A. B. C. D.

95 99 68 34

0.4987 0.9987 0.0013 0.5013

Chapter 6: Continuous Distributions 187 B

65.

M Calc

C

A. B. C. D. 66.

M Calc

D

67.

H Calc

0.3849 0.8849 0.1151 0.6151

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. B. C. D.

68.

0.4772 0.9772 0.0228 0.5228

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. B. C. D.

H Calc

A

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?

404.5 395.5 405.0 395.0

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 only 1% of the values are greater than X. A. B. C. D.

446.6 353.4 400.039 405

188

Test Bank C

69.

H Calc

C

A. B. C. D. 70.

M Calc

B

71.

H Calc

0.3944 0.8944 0.1056 0.6056

The E.P.A. has reported that the average fuel cost for a particular type of automobile is $800 with a standard deviation of $80. Fuel cost is assumed to be normally distributed. If one of these cars is randomly selected, what is the probability that the fuel cost for this car exceeds $760? A. B. C. D.

72.

432.9 396 367.1 404

The E.P.A. has reported that the average fuel cost for a particular type of automobile is $800 with a standard deviation of $80. Fuel cost is assumed to be normally distributed. If one of these cars is randomly selected, what is the probability that the fuel cost for this car exceeds $900? A. B. C. D.

M Calc

B

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 5% of the values are less than X.

0.1915 0.6915 0.3085 0.8085

The E.P.A. has reported that the average fuel cost for a particular type of automobile is $800 with a standard deviation of $80. Fuel cost is assumed to be normally distributed. We would expect that only 10% of these cars would have an annual fuel cost greater than _______. A. B. C. D.

820.0 902.4 808.0 812.8

Chapter 6: Continuous Distributions 189 A

73.

M Calc

C

The E.P.A. has reported that the average fuel cost for a particular type of automobile is $800 with a standard deviation of $80. Fuel cost is assumed to be normally distributed. If a car is randomly selected, what is the probability that fuel cost would be between $700 and $900? A. B. C. D.

74.

0.7888 0.8944 0.3944 0.1056

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 will not have a net loss is _____________.

M BCalc

A. B. C. D.

B

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 will have a net loss is _____________.

75.

0.4772 0.0228 0.9772 0.9544

M BCalc

A. B. C. D.

A

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 profit will be between $12,000 and $15,000 is _____________.

76.

M BCalc

A. B. C. D.

0.4772 0.0228 0.9772 0.9544

0.1859 0.3413 0.8413 0.4967

190

Test Bank C

77.

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 _____________.

M BCalc

A. B. C. D.

A

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 workdays is ______.

78.

0.1859 0.3413 0.8413 0.4967

M BCalc

A. B. C. D.

D

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 215 workdays is _____.

79.

0.0668 0.4332 0.5000 0.9332

M BCalc

A. B. C. D.

A

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 not be completed within 215 work-days is _____.

80.

M BCalc

A. B. C. D.

0.0668 0.4332 0.5000 0.9332

0.0668 0.4332 0.5000 0.9332

Chapter 6: Continuous Distributions 191 C

81.

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 ____ workdays is 0.99.

M BCalc

A. B. C. D.

B

The length of steel rods produced by a shearing process are normally distributed with  = 120 inches and  = 0.05 inch. Industry standards require the rods to be between 119.90 and 120.15 inches, inclusively. The probability that a rod produced by this process will conform to industry standards is ______________.

82.

211 187 223 200

M BCalc

A. B. C. D.

C

The length of steel rods produced by a shearing process are normally distributed with  = 120 inches and  = 0.05 inch. Industry standards require the rods to be between 119.90 and 120.15 inches, inclusively. Any rod longer than 120.15 inches is re-sheared. The probability that a rod produced by this process will require re-shearing is ___________.

83.

0.9542 0.9759 0.9974 0.6826

M BCalc

A. B. C. D.

B

The length of steel rods produced by a shearing process are normally distributed with  = 120 inches and  = 0.05 inch. Industry standards require the rods to be between 119.90 and 120.15 inches, inclusively. Any rod shorter than 119.90 inches is scrapped (used in the next melt). The probability that a rod produced by this process will be scrapped is ___________.

84.

M BCalc

A. B. C. D.

0.0458 0.0228 0.0013 0.0241

0.0458 0.0228 0.0013 0.0241

192

Test Bank A

85.

The weights of aluminum castings produced by a process are normally distributed with  = 2 pounds and  = 0.10 pound. Design specifications require the castings to weigh between 1.836 and 2.164 pounds, inclusively. The probability that a casting produced by this process will conform to design specifications is _________.

M BCalc

A. B. C. D.

C

The weights of aluminum castings produced by a process are normally distributed with  = 2 pounds and  = 0.10 pound. Design specifications require the castings to weigh between 1.836 and 2.164 pounds, inclusively. Any casting weighing less than 1.836 pounds is scrapped. The probability that a casting produced by this process will be scrapped, due to under-weight, is _________.

86.

0.8990 0.4495 0.9974 0.9500

M BCalc

A. B. C. D.

C

The weights of aluminum castings produced by a process are normally distributed with  = 2 pounds and  = 0.10 pound. Design specifications require the castings to weigh between 1.836 and 2.164 pounds, inclusively. Any casting weighing more than 2.164 pounds is re-worked. The probability that a casting produced by this process will be re-worked, due to over-weight, is _________.

87.

0.1010 0.4495 0.0505 0.0010

M BCalc

A. B. C. D.

B

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 _______.

E Calc

88.

A. B. C. D.

0.0010 0.1010 0.0101 0.0505

20 16 3.2 8

Chapter 6: Continuous Distributions 193 C

89.

M Calc

B

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 standard deviation of _______. A. B. C. D.

90.

16 3.2 1.79 0.16

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 _______.

M Term

A. B. C. D.

B

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 12 successes or more, we should find _______.

91.

P(X>12) P(X>12.5) P(X>11.5) P(X12) P(X>11.5) P(X>12.5) P(X