Question

A soft drink dispensing machine uses plastic cups that hold a maximum of 16 ounces. The machine is set to dispense a mean of 14.5 ounces of liquid. The amount of liquid that is actually dispensed varies. It is normally distributed with a standard deviation of 0.5 ounces. Use the Empirical Rule (68%-95%-99.7%) to answer these questions.

(c) What percentage of the time does the machine dispense more than 16 ounces of liquid?   % (two decimal places)

Answer 1

According to the empirical rule, 68%, 95% and 99.7% of data values are within 1, 2 and 3 standard deviations of mean.

here, mean = 14.5 ounces

Standard deviation = 0.5 ounces

14 + 3x0.5 = 16

16 ounces is 3 standard deviations above mean

From empirical rule, we know that 99.7% is inside 3 standard deviations of mean. this means that the remaining 100 - 99.7 = 0.3% values are either below 3 standard deviations or above 3 standard deviations from mean.

Percentage of the time does the machine dispense more than 16 ounces of liquid = 0.3/2 = 0.15%