Let X Poisson() where = 100. Consider the probability p = P(X115).

Suppose we are interested in finding an upper bound on p. That is, we'd like to find a number b such that p b.

(a) Find an upper bound using Markov's inequality.

(b) Find an upper bound using Chebyshev's inequality.

(c) Find an approximate value of p using the central limit theorem.

(d) The true value of p is about 0.063. Which value from (a),(b),(c) is the closest?