Chapter 6, Problem 34PS

The fill amount in 2-liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of $0.05$ liter. If bottles contain less than $95\%$ of the listed net content (1.90 liters, in this case), the manufacturer may be subject to penalty by the state office of consumer affairs. Bottles that have a set content above 2.10 liters may cause excess spillage upon opening. What proportion of the bottles will contain

a. between 1.90 and 2.0 liters?

b. between 1.90 and 2.0 liters?

c. below 1.90 liters or above 2.10 liters?

d. At least how much soft drink is contained in $99\%$ of the bottles?

e. Ninety-nine percent of the bottles contain an amount that is between which two values (symmetrically distributed) around the mean?