BA6933 CHAPTER 6

  1. Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable follows a(n) _____ distribution.         uniform 
  2. There is a lower limit but no upper limit for a random variable that follows the _____ probability distribution   exponential   
  3. The form of the continuous uniform probability distribution is   rectangular     
  4. The mean, median, and mode have the same value for which of the following probability distributions?      normal          
  5. The probability distribution that can be described by just one parameter is the _____ distribution.   exponential   
  6. A continuous random variable may assume   all values in an interval or collection of intervals
  7. For a continuous random variable x, the probability density function f(x) represents _____   the height of the function at x                                      
  8. What type of function defines the probability distribution of ANY continuous random variable?   Probability density function      
  9. For any continuous random variable, the probability that the random variable takes on exactly a specific value is _____.  0
  10. The uniform probability distribution is used with   a continuous random variable   
  11. A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is _____.  the same for each interval                             
  12. For a uniform probability density function, the height of the function   is the same for each value of x
  13. A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is _  1/(b − a)
  14. The probability density function for a uniform distribution ranging between 2 and 6 is _____.  .25
  15. The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 and 95 is _____.   .5
  16. The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability density function has what value in the interval between 6 and 10?  .25
  17. The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product between 7 and 9 minutes is _____.   .50
  18. The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in less than 6 minutes is ____   0
  19. The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in 7 minutes or more is _____.   .75
  20. The assembly time for a product is uniformly distributed between 6 and 10 minutes. The expected assembly time (in minutes) is _____.  8
  21. A normal probability distribution _____.   is a continuous probability distribution
  22. The highest point of a normal curve occurs at   the mean 
  23. Larger values of the standard deviation result in a normal curve that is   wider and flater
  24. A standard normal distribution is a normal distribution with    a mean of 0 and a standard deviation of 1
  25. In a standard normal distribution, the range of values of z is from   minus infinity to infinity
  26. For a standard normal distribution, a negative value of z indicates   the z is to the left of the mean
  27. For the standard normal probability distribution, the area to the left of the mean is _____   0.5
  28. The standard deviation of a standard normal distribution _____   is always equal to 1
  29. For a standard normal distribution, the probability of z ≤ 0 is ____   .5
  30. Assume z is a standard normal random variable. Then P(1.20 ≤ z ≤ 1.85) equals _____.   .0829
  31. Assume z is a standard normal random variable. Then P(-1.96 ≤ z ≤ -1.4) equals __   .0558
  32. Assume z is a standard normal random variable. Then P(-1.20 ≤ z ≤ 1.50) equals _____.   .8181
  33. Assume z is a standard normal random variable. Then P(-1.5 ≤ z ≤ 1.09) equals _____.  .7953
  34. Assume z is a standard normal random variable. Then P(z ≥ 2.11) equals   .0174
  35. Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1112?   1.22
  36. Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1401?   1.08
  37. Given that z is a standard normal random variable, what is the value of z if the area to the left of z is .9382?    1.54
  38. Assume z is a standard normal random variable. What is the value of z if the area between -z and z is .754?   1.16
  39. Assume z is a standard normal random variable. What is the value of z if the area to the right of z is .9803?   -2.06
  40. For a standard normal distribution, the probability of obtaining a z value between -2.4 and -2.0 is ____   .0146
  41. For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is _____.   .9452
  42. For a standard normal distribution, the probability of obtaining a z value between -1.9 and 1.7 is _   .9267
  43. Suppose x is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is   .9190
  44. Suppose x is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is   .0029
  45. Suppose x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is    0
  46. Suppose x is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is _____.  .0069
  47. The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?   50%
  48. Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.

    Refer to Exhibit 6-1. The probability density function has what value in the interval between 20 and 28?   .125
  49. Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
    Refer to Exhibit 6-1. The probability that x will take on a value between 21 and 25 is_____   .5
  50. Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.

    Refer to Exhibit 6-1. The mean of x is _____.  24
  51. Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.

    Refer to Exhibit 6-1. The variance of x is approximately __   5.333
  52. The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.

    Refer to Exhibit 6-2. What is the random variable in this experiment?   time travel
  53. The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.

    Refer to Exhibit 6-2. The probability that she will finish her trip in 80 minutes or less is ____ .8
  54. The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.

     Refer to Exhibit 6-2. The probability that her trip will take longer than 60 minutes is _____. .60
  55. f(x) = (1/10) e^-x/10
    x ≥ 0
    Refer to Exhibit 6-7. The mean of x is _____. 10
  56. f(x) = (1/10) e^-x/10
    x ≥ 0
    Refer to Exhibit 6-7. The probability that x is less than 5 is _____. .3935
  57. f(x) = (1/10) e^-x/10
    x ≥ 0
    Refer to Exhibit 6-7. The probability that x is between 3 and 6 is _____.  .1920
  58. Excel’s NORM.S.DIST function can be used to compute ____   cumulative probabilities for a standard normal z value
  59.  Excel’s NORM.S.INV function can be used to compute ____   the standard normal z value given a cumulative probability
  60. Excel’s NORM.DIST function can be used to compute    cumulative probabilities for a normally distributed x value
  61. Excel’s NORM.INV function can be used to compute  the normally distributed x value given a cumulative probability
  62. When using Excel’s EXPON.DIST function, one should choose TRUE for the third input if _____ is desired.    a cumulative probability
  63. About 95.4% of the values of a normal random variable are within approximately how many standard deviations of its mean?   ±2
  64. Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable follows a(n) _____ distribution    Uniform
  65. There is a lower limit but no upper limit for a random variable that follows the _____ probability distribution   Exponential
  66. The form of the continuous uniform probability distribution is   rectangular
  67. The mean, median, and mode have the same value for which of the following probability distributions?   Normal
  68. The probability distribution that can be described by just one parameter is the _____ distribution.  Exponential
  69. A continuous random variable may assume      all values in an interval or collection of intervals
  70. For a continuous random variable x, the probability density function f(x) represents   the height of the function at x
  71. What type of function defines the probability distribution of ANY continuous random variable?  Probability density function
  72. For any continuous random variable, the probability that the random variable takes on exactly a specific value is   0
  73. The uniform probability distribution is used with    a continuous random variable
  74. The standard deviation of a standard normal distribution    is always equal to 1
  75. Assume that z is a standard normal random variable. Then P(-1.5 < (or equal to) z < (or equal to) 1.09 equals   .7953
  76. The expected value of equals the mean of the population from which the sample is drawn   for any sample size
  77. Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is .1112?   1.22
  78. Given that z is a standard normal random variable, what is the value of z if the area to the left of z is .9382?    1.54
  79. Assume z is a standard normal random variable. What is the value of z if the area between -z and z is .754?   1.16
  80. For a standard normal distribution, the probability of obtaining a z value between -2.4 and -2.0 is    0.146
  81. The basis for using a normal probability distribution to approximate the sampling distribution of and is    the central limit theorem
  82. The standard deviation of is referred to as the    standard error of the proportion
  83. The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.   Infinite
  84. The standard deviation of a point estimator is the             standard error
  85. The finite correction factor should be used in the computation of () when n/N is greater than   0.05
  86. A numerical measure from a population, such as a population mean, is called   a parameter
  87. A sample statistic, such as a sample mean, that estimated the value of the corresponding population parameter is known as a _   point estimator
  88. In computing the standard error of the mean, the finite population correction factor is NOT used when   n/N < (or equal to) 0.05
  89. From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is ___   less than 2
  90. Random samples of size 81 are taken from a process (an infinite population) whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are_   200 and 2
  91. As the degrees of freedom increase, the t distribution approaches the _____ distribution   normal
  92. The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the    confidence coefficient
  93. To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT    degrees of freedom
  94. The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to _____.   0.50
  95. The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 – p) equal or exceed _____  5
  96. We can reduce the margin of error in an interval estimate of p by doing any of the following EXCEPT   using a planning value p* closer to .5
  97. In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with _____ degrees of freedom.   n-1
  98. The mean of the t distribution is   0
  99. A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is    19.2 to 20.8  
  100. The t value with a 95% confidence and 25 degrees of freedom is _____. 2.064      
  101. The z value for a 97% confidence interval estimation is  2.17                 
  102. The sampling distribution of the sample mean _____. sample mean deviation
  103. The mean of the t distribution is _____. 0
  104. The difference between the value of the sample statistic and the value of the corresponding population parameter is called the _____. sampling error
  105. Stratified random sampling is a method of selecting a sample in which The population is first divided into groups, and then random samples are drawn from each group
  106. In point estimation, data from the _____. sample are used to estimate the population parameter
  107. If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the _____ width of the confidence interval to increase
  108. If the margin of error in an interval estimate of μ is 6.8, the interval estimate equals _____.  ± 6.8
  109. If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____. 0.9
  110. From a population that is normally distributed with an unknown standard deviation, a sample of 27 elements is selected. For the interval estimation of μ, the proper distribution to use is the _____. t distribution with 26 degrees of freedom
  111. For the interval estimation of μ when σ is assumed known, the proper distribution to use is the _____ standard normal distribution
  112. Convenience sampling is an example of _____. a nonprobability sampling technique
  113. As the sample size increases, the variability among the sample means _____. decreases
  114. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____. becomes smaller
  115. An interval estimate is used to estimate __ a population parameter
  116. A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately normal because _____. of the central limit theorem
  117. A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is __ approximately normal because of the central limit theorem
  118. A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to .90, the interval for μ _____. becomes narrower
  119. Which of the following statements about a discrete random variable and its probability distribution is true? Values of f(x) must be greater than or equal to zero.
  120. Which of the following is a characteristic of a binomial experiment? The trials are independent.
  121. Which of the following is NOT a characteristic of the normal probability distribution? The standard deviation must be 1.
  122. The starting salaries of individuals with an MBA degree are normally distributed with a mean of $55,000 and a standard deviation of $5,000. What percentage of MBAs will have starting salaries of $49,000 to $61,000? 76.99%
  123. The number of customers who enter a store during one day is an example of _____. a discrete random variable
  124. The mean of a standard normal probability distribution ____ is always equal to 0
  125. The binomial probability distribution is used with _____. a discrete random variable
  126. The ages of students at a university are normally distributed with a mean of 20. What percentage of the student body is at least 20 years old? 50%
  127. The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a race. If there are 8 horses in a particular race, how many “Top Three” outcomes are there? 336
  128. Suppose ten percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is _____. 10
  129. If P(A) = 0.5, P(B) = 0.25, and P(A ∩B) = 0.2, then P(B | A) =_____. 0.40
  130. If P(A) = 0.36, P(B) = 0.85, and P(A ∩ B) = 0.28; then P(A ∪ B) = ____ 0.93
  131. If A and B are independent events with P(A) = 0.2 and P(B) = 0.8, then P(A ∩ B) = _____. 0.16
  132. Highway patrol officers measure the speed of automobiles on a highway using radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a _____. continuous random variable
  133. For a standard normal distribution, the probability of obtaining a z value between –1.30 and 1.90 is _____. 0.0681
  134. For a standard normal distribution, a negative value of z indicates _____ the z is to the left of the mean
  135. For a standard normal distribution the probability of obtaining a z value that is ≥ 2.41 is _____ 0.0080
  136. Events A and B are mutually exclusive with P(A) = 0.10 and P(B) = 0.40. The probability of the complement of event B equals _____. 0.60
  137. Assume that you have a binomial experiment with p = 0.8 and a sample size of 100. The expected value of this distribution is _____. 0.80
  138. Assume that you have a binomial experiment with p = 0.6 and a sample size of 50. The variance of this distribution is _____. 12
  139. An experiment consists of three steps. There are three possible results on the first step, four possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is _____. 24
  140. An experiment consists of four outcomes with P(E1) = 0.3, P(E2) = 0.4, and P(E3) = 0.2. The probability of outcome E4 is _____. 0.100
  141. A standard normal distribution is a normal distribution with _____. a mean of 0 and a standard deviation of 1
  142. A normal probability distribution _____. is a continuous probability distribution
  143. _____ can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean, regardless of the shape of the distribution. Chebyshev’s theorem
  144. _____ can be used to determine the percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution. Empirical Rule
  145. Which of the following variables uses the ratio scale of measurement? Time
  146. Which of the following variables uses the interval scale of measurement? SAT scores
  147. Which of the following values of r indicates the strongest correlation? -0.91
  148. Which of the following symbols represents the size of a population? N
  149. Which of the following symbols represents the mean of a population? μ
  150. Which of the following is an example of quantitative data? the number of people in a waiting line

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