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Homework answers / question archive / 1)The volume of liquid in an unopened 1-litre can of paint is an example of ___
1)The volume of liquid in an unopened 1-litre can of paint is an example of ___.
a) the binomial distribution
b) the normal distribution
c) a continuous random variable
d) a discrete random variable
e) a constant
2. The number of defective parts in a lot of 25 parts 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
3. 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 |
The mean of this distribution is ___.
a) -$400
b) $0
c) $200
d) $400
e) $500
4. 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 |
The standard deviation of this distribution is ___.
a) -$400
b) $663
c) $800,000
d) $894
e) $2000
5. 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
6. 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 |
The mean (average) value of x is ___.
a) 1.0
b) 1.5
c) 2.0
d) 2.5
e) 3.0
7. 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 |
The standard deviation of x is ___.
a) 0.80
b) 0.89
c) 1.00
d) 2.00
e) 2.25
8. 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.
9. 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
10. 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
11. A Bernoulli process (each trial) has exactly ___ possible outcomes.
a) 8
b) 4
c) 2
d) 1
e) 6
12. If x is the number of successes in an independent series of 10 trials, then x has a ___ distribution.
a) hypergeometric
b) Poisson
c) normal
d) binomial
e) exponential
13. 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
14. 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
15. 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
16. 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
17. Twenty five items are sampled. Each of these has the same probability of being defective. The probability that exactly 2 of the 25 are defective 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
18. A fair coin is tossed 5 times. What is the probability that exactly 2 heads are observed?
a) 0.313
b) 0.073
c) 0.400
d) 0.156
e) 0.250
19. 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
20. 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
21. 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, 2013. 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
22. 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, 2013. 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
23. 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, 2013. 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
24. 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, 2013. 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
25. 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
26. 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
27. 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
28. 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
29. If x is a binomial random variable with n=8 and p=0.6, the mean value of x is ___.
a) 6
b) 4.8
c) 3.2
d) 8
e) 48
30. If x is a binomial random variable with n=8 and p=0.6, the standard deviation of x is ___.
a) 4.8
b) 3.2
c) 1.92
d) 1.39
e) 1.00
31. If x is a binomial random variable with n=8 and p=0.6, what is the probability that x is equal to 4?
a) 0.500
b) 0.005
c) 0.124
d) 0.232
e) 0.578
32. 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
33. 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
34. For the Poisson distribution of a random variable lambda (λ) is 5 occurrences per ten-minute time interval. If we want to analyze the number of occurrences per hour, we must use an adjusted value for lambda equal to ___.
a) 5
b) 60
c) 30
d) 10
e) 20
35. On Saturdays, cars arrive at Sam Schmitt's Scrub and Shine Car Wash 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
36. On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash 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
37. The Poisson distribution is being used to approximate a binomial distribution. If n=40 and p=0.06, what value of lambda would be used?
a) 0.06
b) 2.4
c) 0.24
d) 24
e) 40
38. 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
39. The number of phone calls arriving at a switchboard in a 10 minute time period would best be modelled with the ___.
a) binomial distribution
b) hypergeometric distribution
c) Poisson distribution
d) hyperbinomial distribution
e) exponential distribution
40. The number of defects per 1,000 feet of extruded plastic pipe is best modelled with the ___.
a) Poisson distribution
b) Pascal distribution
c) binomial distribution
d) hypergeometric distribution
e) exponential distribution
41. The hypergeometric distribution is similar to the binomial distribution except that ___.
a) sampling is done with replacement in the hypergeometric
b) sampling is done without replacement in the hypergeometric
c) x does not represent the number of successes in the hypergeometric
d) there are more than two possible outcomes in the hypergeometric
42. The probability of selecting 2 male employees and 3 female employees for promotions in a small company would best be modelled with the ___.
a) binomial distribution
b) hypergeometric distribution
c) Poisson distribution
d) hyperbinomial distribution
e) exponential distribution
43. The probability of selecting 3 defective items and 7 good items from a warehouse containing 10 defective and 50 good items would best be modelled with the ___.
a) binomial distribution
b) hypergeometric distribution
c) Poisson distribution
d) hyperbinomial distribution
e) exponential distribution
44. Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women. What is the probability that all three people selected are men?
a) 0.05
b) 0.33
c) 0.11
d) 0.80
e) 0.90
45. Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women. What is the probability that one man and two women are selected?
a) 0.15
b) 0.06
c) 0.33
d) 0.48
e) 0.58
46. 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
47. 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
48. 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
49. 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
50. 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
51. 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
52. 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
53. 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
54. One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the ten 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
55. One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the ten 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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