3.80.* The Russian mathematician Tchebysheff proved that for any k > 1, the proportion of observations that fall more than k standard deviations from the mean can be no greater than 1/k2. This holds for any distribution, not just bell-shaped ones.

(a) Find the upper bound for the proportion of observations falling (i) more than 2 standard deviations from the mean, (ii) more than 3 standard deviations from the mean, (iii) more than 10 standard deviations from the mean.

(b) Compare the upper bound for k = 2 to the approximate proportion falling more than 2 standard deviations from the mean in a bell-shaped distribution.Why is there a difference?