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Homework answers / question archive / 1)Variables which take on values only at certain points over a given interval are called continuous random variables           2

1)Variables which take on values only at certain points over a given interval are called continuous random variables           2

Statistics

1)Variables which take on values only at certain points over a given interval are called continuous random variables

 

 

 

 

 

2. A variable that can take on values at any point over a given interval is called a discrete random variable

 

 

 

 

 

3.   The number of visitors to  a website each day is an example of a discrete random variable

 

 

 

 

 

4.   The amount of time a patient waits in a doctor's office is an example of a continuous random variable

 

 

 

 

 

5. The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

 

 

 

 

 

6. To compute the variance of a discrete distribution, it is not necessary to know the mean of the distribution.

 

 

 

 

 

7. The variance of a discrete distribution increases if we add a positive constant to each one of its value.

 

 

 

 

8. In a binomial experiment, any single trial contains only two possible outcomes and successive trials are independent.

 

 

 

 

 

9. In a binomial distribution, p, the probability of getting a successful outcome on any single trial, increases proportionately with every success.                          

 

 

 

 

 

10. The assumption of independent trials in a binomial distribution is not a great concern if the sample size is smaller than 1/20th of the population size.

 

 

 

 

 

11. For a binomial distribution in which the probability of success is p = 0.5, the variance is twice the mean.

 

 

 

 

 

12. The Poisson distribution is a continuous distribution which is very useful in solving waiting time problems

 

 

 

 

 

13. Both the Poisson and the binomial distributions are discrete distributions and both have a given number of trials.

 

 

 

 

 

14. The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

 

 

 

 

 

15. For the Poisson distribution the mean represents twice the value of the standard deviation..

 

 

 

 

 

16. A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Mexico.

 

 

 

 

 

17. For the Poisson distribution the mean and the variance are the same.

 

 

 

 

 

18. Poisson distribution describes the occurrence of discrete events that may occur over a continuous interval of time or space.

 

 

 

 

19. A Poisson distribution is characterized by one parameter. 

 

 

 

 

20. A hypergeometric distribution applies to experiments in which the trials represent sampling with replacement.

 

 

 

 

21. As in a binomial distribution, each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes, i.e., either a success or a failure. 

 

 

 

 

 

22. The number of successes in a hypergeometric distribution is unknown

 

 

 

 

 

23. In a hypergeometric distribution the population, N, is finite and known.   

 

 

 

 

 

 

Multiple Choice

 

 

 

24. The volume of liquid in an unopened 1-gallon can of paint is an example of _________.

a) the binomial distribution

b) both discrete and continuous variable

c) a continuous random variable

d) a discrete random variable

e) a constant

 

 

 

 

 

25. The number of  finance majors within the School of Business is an example of _______.

a) a discrete random variable

b) a continuous random variable

c) the Poisson distribution

d) the normal distribution

e) a constant

 

 

 

 

26. The speed at which a jet plane can fly is an example of _________.

a) neither discrete nor continuous random variable

b) both discrete and continuous random variable

c) a continuous random variable

d) a discrete random variable

e) a constant

 

 

 

 

27. In American Roulette, there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (or winning -1) is 20/38. Let x be the player profit per game. The mean (average) value of x is approximately_______________.

a) 0.0526

b) -0.0526

c) 1

d) -1

e) 0

 

 

 

 

28. A recent analysis of the number of rainy days per month found the following outcomes and probabilities.

Number of Raining Days (x)

P(x)

3

.40

4

.20

5

.40

The mean of this distribution is _____________.

a) 2

b) 3

c) 4

d) 5

e) <1

 

 

 

 

29.

A recent analysis of the number of rainy days per month found the following outcomes and probabilities.

Number of Raining Days (x)

P(x)

3

.40

4

.20

5

.40

The standard deviation of this distribution is _____________.

a) .800

b) .894

c) .400

d) 4.00

e) .457

 

 

 

 

 

30. You are offered an investment opportunity.  Its outcomes and probabilities are presented in the following table.

x

P(x)

-$1,000

.40

$0

.20

+$1,000

.40

Which of the following statements is true?

a) This distribution is skewed to the right.

b) This is a binomial distribution.

c) This distribution is symmetric.

d) This distribution is skewed to the left.

e) This is a Poisson distribution

 

 

 

 

 

31. A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day.  In this distribution, x represents the number of sodas which an adult drinks.

x

P(x)

0

0.30

1

0.10

2

0.50

3

0.10

The mean (average) value of x is _______________.

a) 1.4

b) 1.75

c) 2.10

d) 2.55

e) 3.02

 

 

 

 

 

32.

A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day.  In this distribution, x represents the number of sodas which an adult drinks.

x

P(x)

0

0.30

1

0.10

2

0.50

3

0.10

The standard deviation of x is _______________.

a) 1.04

b) 0.89

c) 1.40

d) .506

e) .588

 

 

 

 

 

33. A market research team compiled the following discrete probability distribution.  In this distribution, x represents the number of automobiles owned by a family.

x

P(x)

0

0.10

1

0.10

2

0.50

3

0.30

Which of the following statements is true?

a) This distribution is skewed to the right.

b) This is a binomial distribution.

c) This is a normal distribution.

d) This distribution is skewed to the left.

e) This distribution is bimodal.

 

 

 

 

 

34. A market research team compiled the following discrete probability distribution for families residing in Randolph County.  In this distribution, x represents the number of evenings the family dines outside their home during a week.

x

P(x)

0

0.30

1

0.50

2

0.10

3

0.10

The mean (average) value of x is _______________.

a) 1.0

b) 1.5

c) 2.0

d) 2.5

e) 3.0

 

 

 

 

 

35. A market research team compiled the following discrete probability distribution for families residing in Randolph County.  In this distribution, x represents the number of evenings the family dines outside their home during a week.

x

P(x)

0

0.30

1

0.50

2

0.10

3

0.10

The standard deviation of x is _______________.

a) 1.00

b) 2.00

c) 0.80

d) 0.89

e) 1.09

 

 

 

 

 

36. If x has a binomial distribution with  p = .5, then the distribution of x is ________.

a) skewed to the right

b) skewed to the left

c) symmetric

d) a Poisson distribution

e) a hypergeometric distribution

 

 

 

 

 

37. The following graph is a binomial distribution with n = 6.

 
 

 

 

 

 

 

 

 

 

 

This graph reveals that ____________.

a) p > 0.5

b) p = 1.0

c) p = 0

d) p < 0.5

e) p = 1.5

 

 

 

 

 

38. The following graph is a binomial distribution with n = 6.

 
 

 

 

 

 

 

 

 

 

 

This graph reveals that ____________.

a)  p > 0.5

b) p = 1.0

c) p = 0

d) p < 0.5

e) p = 1.5

 

 

 

 

 

39. The following graph is a binomial distribution with n = 6.

 
 

 

 

 

 

 

 

 

 

 

This graph reveals that ____________.

a) p = 0.5

b) p = 1.0

c) p = 0

d) p < 0.5

e) p = 1.5

 

 

 

 

40. If x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____.

a) 6

b) 4.8

c) 3.2

d) 8

e) 48

 

 

 

 

 

41. If x is a binomial random variable with n=10 and p=0.8, the standard deviation of x is _________.

a) 8.0

b) 1.26

c) 1.60

d) 64.0

e) 10

 

 

 

 

 

 

42. If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?

a) .0055

b) .0063

c) .124

d) .232

e) .994

 

 

 

 

43. Twenty five individuals are randomly selected out of 100 shoppers leaving a local bedding store. Each shopper was asked if they made a purchase during their visit.  Each of the shoppers  has the same probability of answering ‘yes’ to having made a purchase. The probability that exactly four of the twenty-five shoppers  made a purchase could best be found by  _______.

a) using the normal distribution

b) using the binomial distribution

c) using the Poisson distribution

d) using the exponential distribution

e) using the uniform distribution

 

 

 

 

44. During a recent sporting event, a quarter is tossed to determine which team picks the starting side. Suppose the referee says the coin will be tossed 3 times and the best two out of three wins If team A calls ‘heads’, what is the probability that exactly two heads are observed in three tosses?

a) .313

b) .375

 

c) .625

d) .875

e) .500

 

 

 

 

45. A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?

a) 0.200

b) 0.031

c) 0.156

d) 0.073

e) 0.001

 

 

 

 

 

46. A student randomly guesses the answers to a five question true/false test.  If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no questions?

a) 0.000

b) 0.200

c) 0.500

d) 0.031

e) 1.000

 

 

 

 

47. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2006.  A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contain errors, P(x = 0) is _______________.

a) 0.8171

b) 0.1074

c) 0.8926

d) 0.3020

e) 0.2000

 

 

 

 

 

48. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2006.  A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contain errors, P(x>0) is _______________.

a) 0.8171

b) 0.1074

c) 0.8926

d) 0.3020

e) 1.0000

 

 

.

 

 

 

49. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2006.  A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contains errors, the mean value of x is __________.

a) 400

b) 2

c) 200

d) 5

e) 1

 

 

 

 

 

50. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2006. A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contains errors, the standard deviation of x is ______.

a) 1.26

b) 1.60

c) 14.14

d) 3.16

e) 0.00

 

 

 

 

 

51. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.  She randomly selects five names from the list for validation.  If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x=0) is ______________.

a) 0.8154

b) 0.0467

c) 0.0778

d) 0.4000

e) 0.5000

 

 

 

 

 

52. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.  She randomly selects five names from the list for validation.  If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x<2) is ______________.

a) 0.3370

b) 0.9853

c) 0.9785

d) 0.2333

e) 0.5000

 

 

 

 

 

53. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.  She randomly selects five names from the list for validation.  If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x>0) is ______________.

a) 0.2172

b) 0.9533

c) 0.1846

d) 0.9222

e) 1.0000

 

 

 

 

 

54. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.  She randomly selects five names from the list for validation.  If 40% of the names on the list are non-authentic, and x is the number on non-authentic names in her sample, the expected (average) value of x is ______________.

a) 2.50

b) 2.00

c) 1.50

d) 1.25

e) 1.35

 

 

 

 

55. A large industrial firm allows a discount on any invoice that is paid within 30 days.  Of all invoices, 10% receive the discount.  In a company audit, 10 invoices are sampled at random.  The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.

a) 0.1937

b) 0.057

c) 0.001

d) 0.3486

e) 0.9298

 

 

 

56. A large industrial firm allows a discount on any invoice that is paid within 30 days.  Of all invoices, 10% receive the discount.  In a company audit, 15 invoices are sampled at random.  The mean (average) value of the number of the 15 sampled invoices that receive discount is _______

a) 1

b) 3

c) 1.5

d) 2

e) 10

 

 

 

 

 

57. In a certain communications system, there is an average of 1 transmission error per 10 seconds. Assume that the distribution of transmission errors is Poisson. The probability of 1 error in a period of one-half minute is approximately ________

a) 0.1493

b) 0.3333

c) 0.3678

d) 0.1336

e) 0.03

 

 

 

 

 

58. It is known that screws produced by a certain company will be defective with probability .01 independently of each other. The company sells the screws in packages of 25 and offers a money-back guarantee that at most 1 of the 25 screws is defective. Using Poisson approximation for binomial distribution, the probability that the company must replace a package is approximately _________

 a) 0.01

b) 0.1947

c) 0.7788

d) 0.0264

e) 0.2211

 

 

 

 

 

59. The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of    5 cars arriving over a five-minute interval is _______.

a) 0.0940

b) 0.0417

c) 0.1500

d) 0.1008

e) 0.2890

 

 

 

 

 

60. The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 3 cars arriving over a five-minute interval is _______.

a) 0.2700

b) 0.0498

c) 0.2240

d) 0.0001

e) 0.0020

 

 

 

 

 

61. Assume that a random variable has a Poisson distribution with a mean of 5 occurrences per ten minutes. The number of occurrences per hour follows a Poisson distribution with λ equal to _________

a) 5

b) 60

c) 30

d) 10

e) 20

 

 

 

 

 

62. On Monday mornings, customers arrive at the coffee shop drive thru at the rate of  6 cars per fifteen-minute interval. Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is _____________.

a) 0.1008

b) 0.0361

c) 0.1339

d) 0.1606

e) 0.5000

 

 

 

 

 

63. On Monday mornings, customers arrive at the coffee shop drive thru at the rate of  6 cars per fifteen minute interval.  Using the Poisson distribution, the probability that five cars will arrive during the next five minute interval is _____________.

a) 0.1008

b) 0.0361

c) 0.1339

d) 0.1606

e) 0.3610

 

 

 

 

 

64. The Poisson distribution is being used to approximate a binomial distribution.  If n=30 and p=0.03, what value of lambda would be used?

a) 0.09

b) 9.0

c) 0.90

d) 90

e) 30

 

 

 

 

65. The Poisson distribution is being used to approximate a binomial distribution.  If n=60 and p=0.02, what value of lambda would be used?

a) 0.02

b) 12

c)  0.12

d) 1.2

e) 120

 

 

 

 

 

66. The number of bags arriving on the  baggage claim conveyor belt  in a 3 minute time period would best be modeled with the _________.

a) binomial distribution

b) hypergeometric distribution

c) Poisson distribution

d) hyperbinomial distribution

e) exponential distribution

 

 

 

 

 

67. The number of defects per 1,000 feet of extruded plastic pipe is best modeled with the ________________.

a) Poisson distribution

b) Pascal distribution

c) binomial distribution

d) hypergeometric distribution

e) exponential distribution

 

 

 

 

 

68. Which of the following conditions is not a condition for  the hypergeometric distribution?

a) the probability of success is the same on each trial

b) sampling is done without replacement

c) there are only two possible outcomes

d) trials are dependent

e) n < 5%N

 

 

 

 

 

69. The hypergeometric distribution must be used instead of the binomial distribution when ______

a) sampling is done with replacement

b)  sampling is done without replacement

c) n≥5% N

d) both b and c

e) there are more than two possible outcomes

 

 

 

 

 

 

 

70. The probability of selecting 2 baseball players and 3 basketball players for an intermural competition at a small sports camp would best be modeled with the _______.

a) binomial distribution

b) hypergeometric distribution

c) Poisson distribution

d) hyperbinomial distribution

e) exponential distribution

 

 

 

 

 

71. The probability of selecting 3 female employees and 7 male employees to win a promotional trip  a company with 10 female and 50 male employees  would best be modeled with the _______.

a) binomial distribution

b) hypergeometric distribution

c) Poisson distribution

d) hyperbinomial distribution

e) exponential distribution

 

 

 

 

 

72. Suppose an interdisciplinary committee of 3 faculty members  is to be selected from a group consisting of 4 men and 5 women.  The probability that all three faculty selected are men is approximately _______

a) 0.05

b) 0.33

c) 0.11

d) 0.80

e) 0.90

 

 

 

 

 

 

73. Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.   The probability that one male faculty and two female faculty are selected is approximately ______

a) 0.15

b) 0.06

c) 0.33

d) 0.48

e) 0.58

 

 

 

 

 

74. Aluminum castings are processed in lots of five each.  A sample of two castings is randomly selected from each lot for inspection.  A particular lot contains one defective casting; and x is the number of defective castings in the sample.  P(x=0) is _______.

a) 0.2

b) 0.4

c) 0.6

d) 0.8

e) 1.0

 

 

 

 

 

75. Aluminum castings are processed in lots of five each.  A sample of two castings is randomly selected from each lot for inspection.  A particular lot contains one defective casting; and x is the number of defective castings in the sample.  P(x=1) is _______.

a) 0.2

b) 0.4

c) 0.6

d) 0.8

e) 1.0

 

 

 

 

 

76. Circuit boards for wireless telephones are etched, in an acid bath, in batches of 100 boards.  A sample of seven boards is randomly selected from each lot for inspection.  A batch contains two defective boards; and x is the number of defective boards in the sample.  P(x=1) is _______.

a) 0.1315

b) 0.8642

c) 0.0042

d) 0.6134

e) 0.6789

 

 

 

 

 

77. Circuit boards for wireless telephones are etched, in an acid bath, in batches of 100 boards.  A sample of seven boards is randomly selected from each lot for inspection.  A particular batch contains two defective boards; and x is the number of defective boards in the sample.  P(x=2) is _______.

a) 0.1315

b) 0.8642

c) 0.0042

d) 0.6134

e) 0.0034

 

 

 

 

 

78. Circuit boards for wireless telephones are etched, in an acid bath, in batches of 100 boards.  A sample of seven boards is randomly selected from each lot for inspection.  A particular batch contains two defective boards; and x is the number of defective boards in the sample.  P(x=0) is _______.

a) 0.1315

b) 0.8642

c) 0.0042

d) 0.6134

e) 0.8134

 

 

 

 

 

79. Ten policyholders file claims with CareFree Insurance.  Three of these claims are fraudulent.  Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.  If x represents the number of fraudulent claims in Earl's sample, P(x=0) is _______________.

a) 0.0083

b) 0.3430

c) 0.0000

d) 0.2917

e) 0.8917

 

 

 

 

 

80. Ten policyholders file claims with CareFree Insurance.  Three of these claims are fraudulent.  Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.  If x represents the number of fraudulent claims in Earl's sample, P(x=1) is _______________.

a) 0.5250

b) 0.4410

c) 0.3000

d) 0.6957

e) 0.9957

 

 

 

 

 

81. If sampling is performed without replacement, the hypergeometric distribution should be used.  However, the binomial may be used to approximate this if _______.

a) n > 5%N

b) n < 5%N

c) the population size is very small

d) there are more than two possible outcomes of each trial

e) the outcomes are continuous

 

 

 

 

 

82. One hundred policyholders file claims with CareFree Insurance.  Ten of these claims are fraudulent.  Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation.  If x represents the number of fraudulent claims in Earl's sample, x has a _______________ distribution.

a) continuous

b) normal

c) binomial

d) hypergeometric

e) exponential

 

 

 

 

 

83. One hundred policyholders file claims with CareFree Insurance.  Ten of these claims are fraudulent.  Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation.  If x represents the number of fraudulent claims in Earl's sample, x has a _______________.

a) normal distribution

b) hypergeometric distribution, but may be approximated by a binomial

c) binomial distribution, but may be approximated by a normal

d) binomial distribution, but may be approximated by a Poisson

e) exponential distribution

 

 

 

 

 

 

 

 

 

 

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