Question

1. By substituting k = 2, write down what the Chebyshev inequality says about the probability that X
will fall within 2 standard deviations of the mean. Do the same for 3 and 4 standard deviations.
2. Substitute k = 1 in the inequality and tell why the resulting inequality is both true and useless.
3. Substitute k =1/2 in the inequality and tell why the resulting inequality is both true and useless. Why will this also happen for any value of k which is between 0 and 1?
4. What does the Chebyshev Inequality tell us about the probability that X will fall more than 2 standard
deviations from the mean? Explain
5. What does the Chebyshev Inequality tell us about the probability that X will fall more than 3 standard
deviations from the mean?