Chapter 5, Problem 39PE

A popular soft drink is sold in $\text{2-liter}$ $\left(\text{2,000-milliliter}\right)$ bottles. Because of variation in the filling process, bottles have a mean of $2,000$ milliliters and a standard deviation of $18$, normally distributed.

1. If the process fills the bottle by more than $\text{30 milliliters}$, the overflow will cause a machine malfunction. What is the probability of this occurring?
2. What is the probability of underfilling the bottles by at least $\text{10 milliliters}$ ?