CFA® Level 1: Bell-Shaped Frequency Distribution | Exam Answer

Bell-Shaped Frequency Distribution

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A bell-shaped, symmetrical frequency distribution has a mean of 50. If 68% of the observations in the distribution fall between 40 and 60, what's the range within which 99% of the observations in the distribution fall?

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For a bell-shaped, symmetrical frequency distribution, approximately 68% of the observations lie within one standard deviation of the mean. The mean equals (40

+ 60)/2 = 50. Therefore, the standard deviation equals 50 - 40 = 10. Now, by the normal rule, 99% of the observations lie within 2.58 standard deviations of the mean. Hence, the requisite range equals [50 - 2.58*10, 50 + 2.58*10] = [24.2, 75.8].

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