Reference no: EM131572264

Question: Suppose that the number of cans of soda pop filled in a day at a bottling plant is a random variable with an expected value of 10,000 and a variance of 1000.

a) Use Markov's inequality (Exercise) to obtain an upper bound on the probability that the plant will fill more than 11,000 cans on a particular day.

b) Use Chebyshev's inequality to obtain a lower bound on the probability that the plant will fill between 9000 and 11,000 cans on a particular day

Exercise: Let X be a random variable on a sample space S such that X(s) ≥ 0 for all s ∈ S. Show that p(X(s) ≥ a) ≤ E(X)/a for every positive real number a. This inequality is called Markov's inequality.