According to Chebyshev's Theorem, what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?

CFA Level 1: Chebyshev's Theorem and Observations within 1.75 Standard Deviations

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Question

According to Chebyshev's Theorem, what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?

Answers

A. Cannot compute because it depends on the shape of the distribution

B. 56%

C. 95%

D. 67%

E. None of these answers

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Explanations

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A. B. C. D. E.

Chebyshev's theorem applies regardless of the shape of the distribution. The minimum proportion that lie within k standard deviations of the mean is at least 1-[1/

(k^2)]. In this case k = 1.75. k^2 = 3.0625. So we get 67%.

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