In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler in Problem 6.30 sets the filling machine so that the mean is 2.02 liters. Under these circumstances, what are your answers in Problem 6.30 (a) through (e)?

Problem 6.30

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 net 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 2.10 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?