Consider the random variable y = the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose the probability distribution of y is as follows. y o 1 2 3 4 p(y) 0.66 0.18 0.12 0.03 ? (a) Only y values of 0, 1, 2, 3, and 4 have probabilities greater than 0. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) (b) How would you interpret p(1) = 0.18? O The proportion of eggs that will be broken in each carton from this population is 0.18. O In the long run, the proportion of cartons that have exactly one broken egg will equal 0.18. 0 If you check a large number of cartons, the proportion that will have at most one broken egg will equal 0.18. O The probability of one randomly chosen carton having broken eggs in it is 0.18. (c) Calculate P(y s 2), the probability that the carton contains at most two broken eggs. Interpret this probability. 0 If you check a large number of cartons, the proportion that will have at most two broken eggs will equal 0.96. O The probability of two randomly chosen cartons having broken eggs in them is 0.96. O The proportion of eggs that will be broken in any two cartons from this population is 0.96. O In the long run, the proportion of cartons that have exactly two broken eggs will equal 0.96. (d) Calculate P(y