答案和详解如下： 1、According to Chebyshev’s Inequality, for any distribution, what is the minimum percentage of observations that lie within three standard deviations of the mean? A) 56%. B) 75%. C) 89%. D) 94%. The correct answer was C) According to Chebyshev’s Inequality, for any distribution, the minimum percentage of observations that lie within k standard deviations of the distribution mean is equal to: 1 – (1/k2). If k = 3, then the percentage of distributions is equal to 1 – (1/9) = 89%. 2、In a skewed distribution, what is the minimum amount of observations that will fall between +/- 1.5 standard deviations from the mean? A) 95%. B) 44%. C) 25%. D) 56%. The correct answer was D) Because the distribution is skewed, we must use Chebyshev’s Inequality, which states that the proportion of observations within k standard deviations of the mean is at least 1 – (1/k2). 1 – (1/1.52) = .5555, or 56% 3、Regardless of the shape of a distribution, according to Chebyshev’s Inequality, what is the minimum percentage of observations that will lie within + or – two standard deviations of the mean? A) 68%. B) 34%. C) 75%. D) 89%.
The correct answer was C) According to Chebyshev’s Inequality, for any distribution, the minimum percentage of observations that lie within k standard deviations of the distribution mean is equal to:
1 – (1/k2), with k equal to the number of standard deviations. If k = 2, then the percentage of distributions is equal to 1 – (1/4) = 75%. 4、In a skewed distribution, what is the minimum proportion of observations between +/- two standard deviations from the mean? A) 95%. B) 84%. C) 25%. D) 75%. The correct answer was D) For any distribution we can use Chebyshev’s Inequality, which states that the proportion of observations within k standard deviations of the mean is at least 1 – (1/k2). 1 – (1/22) = 0.75, or 75%. Note that for a normal distribution, 95% of observations will fall between +/- 2 standard deviations of the mean. 5、Assume a sample of beer prices is negatively skewed. Approximately what percentage of the distribution lies within plus or minus 2.40 standard deviations of the mean? A) 58.3%. B) 17.36%. C) 95.5%. D) 82.6%. The correct answer was D) Use Chebyshev’s Inequality to calculate this answer. Chebyshev’s Inequality states that for any set of observations, the proportion of observations that lie within k standard deviations of the mean is at least 1 – 1/k2. We can use Chebyshev’s Inequality to measure the minimum amount of dispersion whether the distribution is normal or skewed. Here, 1 – (1 / 2.42) = 1 - 0.17361 = 0.82639, or 82.6%. | 
发表于 2008-4-8 18:11
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