Let y denote the number of broken eggs In a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y 0 1 2 3 4 p(y) 0.65 0.20 0.10 0.04 v (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) (b) How would you interpret [9(1) - 0.20? "'- If you check a large number of cartons, the proportion that will have at most one broken egg will equal 0.20. "'- In the long run, the proportion of cartons that have exactly one broken egg will equal 0.20. "'- The probability of one randomly chosen carton having broken eggs in it is (1.29. "'- The proportion of eggs that will be broken in each carton from this population is 0.20. ((2) Calculate My 5 2), the probability that the carton contains at most two broken eggs. Interpret this probability. "'- The probability of two randomly chosen cartons having broken eggs in them is 0.95. "' The proportion of eggs that will be broken in any two cartons from this population is 0.95. "'- If you check a large number of cartons, the proportion that will have at most two broken eggs will equal 0.95. "'- In the long run, the proportion of cartons that have exactly two broken eggs will equal 0.95. (:1) Calculate P(y