Question

Suppose that the distribution of monthly revenues of a new startup business is not symmetric. According to Chebyshev's Theorem, at least approximately what percentage of the revenues are within k=3.3 standard deviations of the mean? Round your answer to the nearest whole number (percent).

Answer 1

Chebyshev's Theorem states that for any distribution, at least 1 - (1/k^2) of the data falls within k standard deviations of the mean, where k is a positive number greater than 1.

In your case, k = 3.3. So, at least 1 - (1/3.3^2) = 1 - (1/10.89) ≈ 0.9084, or approximately 90.84% of the revenues are within 3.3 standard deviations of the mean. Rounding to the nearest whole number, this is approximately 91%.