Suppose that the weights of large eggs are normally distributed with a mean of 57 grams and a standard deviation of 3 grams.
a) Suppose we select 100 cartons(each containing 12 eggs) at random. The 12 eggs in each carton can be assumed to be a random sample from the population. For each carton, we calculate the mean weight of the 12 eggs inside. Sketch what you would expect to be the distribution of these 100 carton means. Why is the distribution the shape it is?
b) What would you expect the mean of these 100 cartons to be?
c) What would you expect the standard deviation of the means of the 100 cartons to be?
d) What percentage of large eggs can be expected to be heavier than 60 grams?
e) What percentage of cartons of eggs can be expected to have a mean weight of heavier than 60 grams?