A random variable can take on four values: 12, 36, 78, 111, each with probability 0.25. The standard deviation of the random variable equals ________.
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A. B. C. D.Explanation
Since all the observations occur with equal probability, the mean of the observations is (12 + 36 + 78 + 111)*0.25 = 59.25. The variance is then given by 0.25*
( [12-59.25]^2 + [36-59.25]^2 + [78-59.25]^2 + [111-59.25]^2) = 1451. The standard deviation is equal to sqrt(1451) = 38.1.