# tif_ch06 - 142 The Normal Distribution and Other Continuous...

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142 The Normal Distribution and Other Continuous Distributions CHAPTER 6: THE NORMAL DISTRIBUTION AND OTHER CONTINUOUS DISTRIBUTIONS 1. In its standardized form, the normal distribution a) has a mean of 0 and a standard deviation of 1. b) has a mean of 1 and a variance of 0. c) has an area equal to 0.5. d) cannot be used to approximate discrete probability distributions. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: standardized normal distribution, properties 2. Which of the following about the normal distribution is NOT true? a) Theoretically, the mean, median, and mode are the same. b) About 2/3 of the observations fall within ± 1 standard deviation from the mean. c) It is a discrete probability distribution. d) Its parameters are the mean, μ , and standard deviation, σ . ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: normal distribution, properties 3. If a particular batch of data is approximately normally distributed, we would find that approximately a) 2 of every 3 observations would fall between ± 1 standard deviation around the mean. b) 4 of every 5 observations would fall between ± 1.28 standard deviations around the mean. c) 19 of every 20 observations would fall between ± 2 standard deviations around the mean. d) all of the above ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: normal distribution, properties

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143 The Normal Distribution and Other Continuous Distributions 4. For some positive value of Z , the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is a) 0.18. b) 0.81. c) 1.16. d) 1.47. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 5. For some value of Z , the probability that a standardized normal variable is below Z is 0.2090. The value of Z is a) – 0.81. b) – 0.31. c) 0.31. d) 1.96. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 6. For some positive value of Z , the probability that a standardized normal variable is between 0 and Z is 0.3340. The value of Z is a) 0.07. b) 0.37. c) 0.97. d) 1.06. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 7. For some positive value of X , the probability that a standardized normal variable is between 0 and + 2 X is 0.1255. The value of X is a) 0.99. b) 0.40. c) 0.32. d) 0.16. ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: normal distribution, value
The Normal Distribution and Other Continuous Distributions 144 8. For some positive value of X , the probability that a standardized normal variable is between 0 and +1.5 X is 0.4332. The value of X is a) 0.10. b) 0.50. c) 1.00. d) 1.50. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: normal distribution, value 9. Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54. ANSWER:

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## This note was uploaded on 05/26/2011 for the course DS 300 taught by Professor Zhixinlui during the Winter '11 term at University of Michigan-Dearborn.

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tif_ch06 - 142 The Normal Distribution and Other Continuous...

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