A graphing calculator may be used wherever possible. However, you need to substantiate your answers for full credit if necessary. If you are to use a decimal for a probability, round your answer to four decimal places. This assignment covers sections 5.1 - 5.3. [1](10) Let X denote the number of broken eggs in a randomly selected carton of one dozen "store brand" eggs at a certain supermarket. Suppose that the probability distribution of X is as follows: X 2 3 4 P(X) 0.95 0.02 0.015 0.01 a) If only X values 0, 1, 2, 3, and 4 have positive probabilities, what is P(X = 4)? b) How would you interpret P(X = 1) = 0.02? c) What is the probability that at least ten eggs are unbroken? d) If two cartons are randomly selected, what is the probability that totally two eggs are found broken? e) Calculate and interpret the mean value / for X. [) Why doesn't the mean p _ " + 1 + 2+ 3 + 4 - = 2.0? 5