Empirical Rule Problem

Question

A soft drink dispensing machine uses plastic cups that hold a maximum of 12 ounces. The machine is set to dispense a mean of x = 10 ounces of liquid. The amount of liquid that is actually dispensed varies. It is normally distributed with a standard deviation of s = 1 ounce. Use the Empirical Rule (68%-95%-99.7%) to answer these questions.

(a) What percentage of the cups contain between 10 and 11 ounces of liquid?

(b) What percentage of the cups contain between 8 and 10 ounces of liquid?

(c) What percentage of the cups spill over because 12 ounces of liquid or more is dispensed?

(d) What percentage of the cups contain between 8 and 9 ounces of liquid?

Answer 1

(a) What percentage of the cups contain between 10 and 11 ounces of liquid?

0.3413447399

(b) What percentage of the cups contain between 8 and 10 ounces of liquid?

0.4772499385

(c) What percentage of the cups spill over because 12 ounces of liquid or more is dispensed?

0.022750062

(d) What percentage of the cups contain between 8 and 9 ounces of liquid?

0.1359051075