A random variable, X, has a mean of 12 and a standard deviation of 14. If another variable, Y, is defined by Y = 2X - 3, the coefficient of variation of Y is
________.
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A. B. C. D.B
You should remember two important points:
1. Multiplying a random variable by a constant multiplies its mean and standard deviation by the same constant.
2. Adding a constant to a random variable increases the mean by the same constant but leaves the standard deviation unchanged.
Using these two rules, the mean of Y equals 2 * 12 - 3 = 21. The standard deviation of Y equals 2 * 14 = 28. The coefficient of variation equals the ratio of the standard deviation to the mean. Thus, the coefficient of variation of Y equals 28 / 21 = 1.33.