One egg dyeing helper was particularly clumsy and cracked many of the eggs. The

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One egg dyeing helper was particularly clumsy and cracked many of the eggs. The probability that he cracked any particular egg was 0.25. You can assume that cracking each egg is independent. Later I opened a carton of 12 dyed eggs prepared by this helper. What is the mean number of cracked eggs 1 should expect to see? What is the variance of the number of cracked eggs in a 12 egg carton? What is t he probability that exactly half of the eggs in the carton are cracked? (Still assuming 12 eggs per carton.) Suppose that the helper dyed 50 cartons of eggs. What distribution would the (sample) average number of cracked eggs per carton in 50 cartons approximately follow? (i.e. let X, be the number of eggs cracked in the i-th carton, then X = 1/50 (X_1 + X_2 + ... + X_50) is the average number of cracked eggs per carton. What distribution does X approximately follow? What is the probability that the average number of cracked eggs per carton is exactly 6? What is the probability that the average number of cracked eggs per carton is more than 2?

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