Crackers are often packaged in boxes that are supposed to contain 16 ounces. However, no manufacturing plant is perfect and so there might be slight errors. For example, Chris' Crunchy Crackers (CCC) has verified that the weight of the crackers in their boxes has a normal distribution with a mean of 16 ounces and a standard deviation of 0.9 ounces. Although this is made up, it's not completely divorced from the truth. 1. You open a box of CCC and realize the weight is 15.6 ounces. What is the probability that a single box will contain 15.6 ounces or less of crackers?

~ Troubled by the low-weight box of crackers, you decide to empty out all the crackers from six boxes and realize the mean weight for the six boxes is 15.6 ounces. What is the probability that six boxes will have a mean weight of 15.6 ounces or less?

~Not satisfied with the information you figured out in #2, you take a case (36 boxes) and empty out all the crackers and find that the mean amount of crackers in all the boxes is 15.6 ounces. What is the probability that case will have a mean weight of 15.6 ounces or less ?

~Draw three normal distributions on the same set of axes or with the same scale to show how the probabilities decrease from box can to six boxes to 36 boxes even though we're looking at "less than 15.6 ounces."

~Use the graphs and your own understanding of the Central Limit Theorem to write a few sentences explaining what is happening here.