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  3. For a certain distribution, the measurement 12.1 is 1.5 standard deviations belo

For a certain distribution, the measurement 12.1 is 1.5 standard deviations belo

游客2024-01-12  23
问题 For a certain distribution, the measurement 12.1 is 1.5 standard deviations below the mean, and the measurement 17.5 is 3.0 standard deviations above the mean. What is the mean of the distribution?
选项 A、13.8
B、13.9
C、14.0
D、14.1
E、14.2
答案 B
解析 If m represents the mean of the distribution and s represents the standard deviation, then the statement "the measurement 12.1 is 1.5 standard deviations below the mean" can be represented by the equation 12.1 = m - 1.5s. Similarly, the statement "the measurement 17.5 is 3.0 standard deviations above the mean" can be represented by the equation 17.5 = m +3.0s.
One way to solve the two linear equations for m is to eliminate the s. To do this, you can multiply the equation 12.1 = m - 1.5s by 2 and then add the result to the equation 17.5 = m + 3.0s to get 41.7 = 3m. Solving this equation for m gives the mean 13.9. Thus the correct answer is Choice B.
This explanation uses the following strategy.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
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