1. Each mating season, birds of a certain species usually lay a clutch of 6 eggs in their nests. A biologist notices, however, that clutch number deviates from the usual when the birds feed on a certain kind of berry containing a narcotic alkaloid. He examines the nests of 7 such birds and finds the following numbers of eggs:
8 2 5 7 4 10 6
a. Is there evidence that the alkaloid causes the birds to lay fewer eggs than usual?
b. Compute the variance of the sample.
2. Show that Chebyshev's theorem is true for the population in Exercise for k = 2 and k = 3.