It has been determined empiracally that for a certain egg producer, the number of cracked or broken eggs X, in a randomly slected box containing six eggs, follows approximately the distribution given in the table below:
X: 0 1 2 3 4 5 6
P(X): 0.9 0.07 0.02 0.005 0.003 0.001 0.001
find the expectation and variance of X.
i) exceeds 175
ii) is at least 150 but does not exceed 190.
indicate any assumptions you have made, and indicate briefly how these might be violated.
This shows how to use central limit theorem to calculate probability.