Chebyshev's rule, states that regardless of how the data are distributed, at least (1 1/k2) 100% of the distribution of a variable will fall within k standard deviations of

the mean (for k > 1). a. For k = 2 and for k = 3, what is the maximum amount of the distribution that will fall within k standard deviations of the mean?

b. Find a distribution that minimizes the portion of the distribution (mass for discrete, density for continuous) that falls within 2 standard deviations of the mean. How does this compare with Chebyshev's rule? Explain.

c. Find a distribution that minimizes the portion of the distribution (mass for discrete, density for continuous) that falls within 3 standard deviations of the mean. How does this compare with Chebyshev's rule? Explain.