Normal Distribution: Finding Standard Deviation - CFA® Level 1 Exam Prep

Calculating Standard Deviation for Normal Distribution

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Question

The probability that a value from a normal distribution will be less than 4 equals 83%. If the distribution has a mean of 2.2, the standard deviation of the distribution must be:

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A. B. C. D.

Explanation

Using the Normal probability tables, the z-value of the observation, X, which can be exceeded with a probability of 17% equals 0.955. We are given that X = 4.

Now, the z-value of a selected observation, X, from a normal distribution with mean M and standard deviation S equals z = (X-M)/S. Therefore, 0.955 = (4 - 2.2)/S.

This gives S = 1.885.

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