Chapter 3.3, Problem 15E

The “fill” problem is important in many industries, such as those making cereal, toothpaste, beer, and so on. If an industry claims that it is selling 12 ounces of its product in a container, it must have a mean greater than 12 ounces, or else the FDA will crack down, although the FDA will allow a very small percentage of the containers to have less than 12 ounces.

(a) If the content X of a container has a $N\left(12.1,{\sigma }^2\right)$ distribution, find $\sigma$ so that $P\left(X<12\right)=0.01$.

(b) If $\sigma =0.05$, find $\mu$ so that $P\left(X<12\right)=0.01$.