A machine takes 6 eggs from a conveyer belt and attempts to place them into a tray. Each egg will fit neatly into the tray if its diameter is between 4.5 and 5.5 cm. a) [2 marks] If the diameter of eggs follows a normal distribution with a mean of 4.9cm and a standard deviation of 0.2 cm. What is the probability that a randomly selected egg will fit neatly in a tray? b) [2 marks] What is the probability that a randomly selected group of 6 eggs will each fit neatly in the tray? c) [2 marks] The tray is labelled minimum total weight of eggs: 360 grams meaning that the average weight of the eggs in the tray has to be more than 60 grams. If the weight of eggs is described by a normal distribution with mean 62 grams and a standard deviation of 2 grams what is the distribution of the mean weight of a sample of 6 eggs? d) [2 marks] What is the probability that a randomly chosen group of 6 eggs weighs at least 360 grams? e) [2 marks] A colleague of yours suggests that to get the overall probability of a group of 6 eggs meeting both the size and weight constraints you should multiply the probability in (b) with the probability in (d). Do you agree? Why or why not?