15. The probability distribution for X, the number of eggs in a bald eagle's nest, is given below. These values are based on long-term historical records of the reproductive practices of bald eagles. X P(X) 0 .25 1 .62 2 .13 a) What is the probability that the mean number of eggs in a random sample of three nests is 1.00? b) Biologists plan to randomly sample 38 nests to determine whether environmental changes have harmed the reproductive capacities of bald eagles. Given the historical probability distribution for X, what are the mean and standard deviation of the sampling distribution of the mean number of eggs per nest based on samples of 38 nests? c) What is the probability that two randomly chosen samples of 38 nests both contain more than 40 eggs?