6.08.2005

Q&A: An analyst thinks that the mean return rate for tax-exempt municipal bonds...

...is 9.1% with a standard deviation of 3%. What is the minimum percentage of return rates for tax-exempt municipal bonds with rates between 3.1% and 15.1%?

A:

  • [3.7%, 14.5%] lie with +/- 2 standard deviations of the mean
    • (15.1-9.1)/3 = 2
    • (9.1-3.1)/3 = 2
  • From Chebyshev's Inequality: 1-1/k^2 = 1-1/2^2 = 75%

Bonus Points

  • It applies to both populations and samples, and for discrete and continuous data, regardless of the shape of the distribution.
    • Empirical Rule only applies to normal distributions. It states 68% within 1s, 95% within 2s, and 99% within 3s.
  • Gives a conservative estimate of the proportion of observations in an interval about the mean.
    • Assume the return is normal, Empirical rule gives 95% > 75%.

Category: Quantitative Analysis > Probability

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