III. Quantitative variables can be continuous variables
I. Categorical variables are the same as qualitative variables.
II. Categorical variables are the same as quantitative variables.
III. Quantitative variables can be continuous variables.
35.A coin is tossed three times. What is the probability that it lands on heads exactly one time? 3/8
36. A coin is tossed three times. What is the probability that it lands on heads exactly two times? 3/8
37. A coin is tossed three times. What is the probability that it lands on heads exactly three times? 1/8
38. Which of the following statements is true?
o The center of a confidence interval is a population parameter
o The center of a confidence interval is a sample statistic
o The bigger the margin of error, the smaller the confidence interval
o The confidence interval is a type of point estimate
o A population mean is an example of point estimate
39. A sample consists of four observations: {1, 3, 5, 7}. What is the sample standard deviation? Корень из 20/3=2.58
40. A card is drawn randomly from a deck of 52 ordinary playing cards. You win $10 if the card is a spade or an ace. What is the probability that you will win the game? 16/52=4/13
41. An achievement test has a mean score of 100 and a standard deviation of 15. If a student’s z-score is 1.20, what was his score on the test? 100+15*1,2=118
42. An achievement test has a mean score of 100 and a standard deviation of 15. If a student’s z-score is - 1.20, what was his score on the test? 100-15*1,2=82
43. Which of the following is a formula for the number of all possible combinations of n objects from a set of N objects
44. Which of the following is a formula for the number of all possible permutations of n objects from a set of N objects
45. Consider a discrete random variable X that can assume the values 0, 1, and 2 with probabilities 0.2, 0.5, and 0.3, respectively. What is the expected value of X? E(x)=0*0,2+1*0,5+2*0,3=1,1
46. Consider a discrete random variable X that can assume the values 0, 1, and 2 with probabilities 0.2, 0.5, and 0.3, respectively. What is the variance of X? 0,49
47. Consider a discrete random variable X that can assume the values 0, 1, and 2 with probabilities 0.2, 0.5, and 0.3, respectively. What is the standard deviation of X? 0,7
48. A random variable is said to be discrete if
o it can assume any real number within an interval
ü the rules of probability apply
o its possible values can be counted or listed
o it can be represented graphically
o it can assume any real number
49. Suppose that X is a random variable that can assume the values 1, 2, and 3. If P(X = 1) = 0.1 and P(X = 2) = 0.2, what is P(X = 3)? P(x=3)=1-0,1-0,2=0,7
50. In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety are: mean=2; s=1,265
51. If you flip a fair coin 5 times, what is the probability you will get exactly two heads? 5/16
52. If you flip a fair coin 5 times, what is the probability you will get exactly three heads? 5/16
53. A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the following distribution:
f (x) 0.24 0.37 0.20 0.11 0.05 0.03
x 0 1 2 3 4 5
What is the probability that a randomly chosen household has at least two personal computers? 0.39
54. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately normal with mean $360 and standard deviation $50. What is P(X >$400)? 0.2119
55. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately normal with mean $360 and standard deviation $50. What is P(X≤ $400)?
56. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately normal with mean $360 and standard deviation $50. What is P(X < $300)?
57. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately normal with mean $360 and standard deviation $50. What is P(X ≥ $300)?
58. Delta Airlines quotes a flight time of 125 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 120 minutes and 140 minutes. What is the probability that the flight will be more than 10 minutes late? 1/4
59. Delta Airlines quotes a flight time of 125 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 120 minutes and 140 minutes. What is the expected flight time? 130 minutes.
60. The random variable x is known to be uniformly distributed between 1.0 and 1.5. Compute P(x = 1.25) 0
61. The random variable x is known to be uniformly distributed between 1.0 and 1.5. Compute P(1.0 ≤ x ≤ 1.25) 1/2
62. The random variable x is known to be uniformly distributed between 1.0 and 1.5. Compute P(1.2 ≤ x ≤ 1.5) 3/5
63. The driving distance for the top 100 golfers on a tour is between 284.7 and 310.6 yards. Assume that the driving distance for these golfers is uniformly distributed over this interval. What is the probability the driving distance for one of these golfers is less than 290 yards? 0.2046
64. The driving distance for the top 100 golfers on a tour is between 284.7 and 310.6 yards. Assume that the driving distance for these golfers is uniformly distributed over this interval. What is the probability the driving distance for one of these golfers is at least 300 yards? 0.4093
65. The driving distance for the top 100 golfers on a tour is between 284.7 and 310.6 yards. Assume that the driving distance for these golfers is uniformly distributed over this interval. What is the probability the driving distance for one of these golfers is between 290 and 305 yards? 0 .5792
66. Which of the following is the formula of converting any normal random variable x with mean μ and standard deviation σ to the standard normal random variable z = (X - μ) / σ
67. Suppose that the probability of an event A is 0.2 and the probability of an event B is 0.4. Also, suppose that the two events are independent. Then the conditional probability P(A|B) is P(A) = 0.2 or P(A) =0
68. Which one of these examples is a continuous random variable?
o The number of new accounts established by a salesperson in a year
o The number of correct guesses on a multiple choice test
o The number of women taller than 68 inches in a random sample of 5 women
o The number of children a randomly selected person has
ü The time it takes a randomly selected student to complete an exam
69. The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What is the expected value of the number of patients who are successfully treated? 32
70. If a random variable X is uniformly distributed on an interval [a, b], then its expected value is equal to E(x)=(a+b)/2
71. If a random variable X is uniformly distributed on an interval [a, b], then its variance is equal to Var(X) = E |X2| − E[X] 2 = 1/12 (b − a) 2
72. The probability density function of a uniformly distributed random variable X has the following form:
73. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. What is the expected number of calls in one hour?
74. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. What is the probability of three calls in five minutes?
- 33 e-5
3!
- e -3
3!
- 53 e-2.5
3!
- 53 e-5
3!
- 2.53 e-2.5
3!
75. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. What is the probability of no calls in five-minute period? e^-2.5 =0 .0821
76. A simple random sample of 49 items from a population with σ = 6 resulted in a sample mean of 32. Provide a 90% confidence interval for the population mean. 30,59 – 33,41
77. A simple random sample of 49 items from a population with σ = 6 resulted in a sample mean of 32. Provide a 95% confidence interval for the population mean. 30,32 – 33,68
78. A simple random sample of 49 items from a population with σ = 6 resulted in a sample mean of 32. Provide a 99% confidence interval for the population mean. 29,789 – 34,211
79. In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a sample of 100 customers. Assume a population standard deviation of $5. If the sample mean is $24.80, what is the 95% confidence interval for the population mean? 23,82 – 25,78
80. A simple random sample of 64 items resulted in a sample mean of 80. The population standard deviation is σ = 15. Compute the 95% confidence interval for the population mean. 76,325 - 83,675
81. Which of the following is NOT considered as a measure of variability of statistical data
ü mode
82. Which of the following is NOT considered as a measure of location of statistical data
o median
o mode
o sample mean
ü standard deviation
o quartile
83. Which of the following numerical measures for a data set determines the value in the middle when the data are arranged in ascending order
ü median
o mode
o sample mean
o standard deviation
o quartile
84. Which of the following numerical measures for a data set determines the value that occurs with greatest frequency
o median
ü mode
o sample mean
o standard deviation
o quartile
85. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the sample mean. 15
86. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the sample median. 16
87. Consider a sample with data values of 10, 20, 21, 12, 17, and 16. Compute the sample median. 16.5
88. Consider a sample with data values of 10, 20, 21, 12, 17, and 16. Compute the sample mean. 16
89. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th percentile. 20
90. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th percentile. 20
91. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 25th percentile. 22,5
92. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 65th percentile. 28
93. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 75th percentile. 29
94. Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the sample mean. 59,73
95. Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the sample median. 57
96. Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the sample mode. 53
97. Which of the following numerical measures for a data set determines the difference between the largest and smallest values
ü range
o median
o sample variance
o standard deviation
o quartile
98. Which of the following numerical measures for a data set determines the difference between the third and first quartiles
o mode
ü interquartile range
o sample variance
o standard deviation
o median
99. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range. 10
100. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the interquartile range. 5
101. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the sample variance. 16
102. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the sample standard deviation. 4
103. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range. 19
104. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the interquartile range. 6,5
105. A bowler’s scores for six games were 182, 168, 184, 190, 170, and 174. Compute the sample range. 22
106. Which of the following numerical measures for a data set determines how far a particular value is from the mean
o median
o mode
o z-score
o interquartile range
ü standard deviation
107. An unusually small or unusually large data value is called …
o variance
o median
ü outlier
o mode
o Z-score
108. A data value can be considered as an outlier if its z-score is
o greater than +1
o less than -2
o greater than +2
o less than -1
ü less than -3
109. A data value can be considered as an outlier if its z-score is
ü greater than +3
o less than -2
o greater than +2
o less than -1
o greater than +1
110. Consider a sample with a mean of 500 and a standard deviation of 100. What is the z-score for the data value of 520. 0,20
111. Consider a sample with a mean of 500 and a standard deviation of 100. What is the z-score for the data value of 650. 1,50
112. Consider a sample with a mean of 500 and a standard deviation of 100. What is the z-score for the data value of 500. 0
113. Consider a sample with a mean of 500 and a standard deviation of 100. What is the z-score for the data value of 450. -0,50
114. Consider a sample with a mean of 500 and a standard deviation of 100. What is the z-score for the data value of 280. -2,20
115. How many permutations of three items can be selected from a group of six. 120
116. How many combinations of three items can be selected from a group of six. 20
117. How many permutations of four items can be selected from a group of seven. 840
118 . How many combinations of four items can be selected from a group of seven. 35
119. A survey of magazine subscribers showed that during the past 12 months 45.8% rented a car for business reasons, 54% rented a car for personal reasons, and 30% rented a car for both business and personal reasons. What is the probability that a subscriber rented a car for business or personal reasons? 69,8%
120. A survey of magazine subscribers showed that during the past 12 months 45.8% rented a car for business reasons, 54% rented a car for personal reasons, and 30% rented a car for both business and personal reasons. What is the probability that a subscriber did not rent a car for either business or personal reasons? 30,2%