Chapter 4.1, Problem 4GA

A standard package of Oreos is supposed to contain 510 grams of chocolatey goodness. But there’s variation in just about anything, including production and packaging, so some packages will contain more and some will contain less. In fact, this is exactly the sort of quantity that tends to be normally distributed. The folks that run Nabisco aren’t stupid, and they know that customers won’t be very happy if they weigh a package of cookies and find that it contains less than the labeled amount. The typical approach to keep that from happening is to design the packaging process so that the mean is something more than 510 grams, with a standard deviation that guarantees that the vast majority of packages contain 510 grams or more.

Using what we know about the connection between probability and percent chance, what’s the probability that a randomly chosen package contains between 514 and 522 grams?