Question

The label on a bottle of liquid detergent shows the contents to be 12 grams per bottle. The production operation fills the bottle uniformly according to the following probability density function:

f(x) =	{	8   11:975 < x < 12:100
		0    elsewhere

where x denotes the grams the bottle will be filled.

a) What is the expected value and the standard deviation of X?

b) What is the probability that a bottle will be filled with between 12 and 12.05 grams?

c) What is the probability that a bottle will be filled with 12.02 or more grams?

d) Quality control accepts a bottle that is filled to within 0.02 grams of the number of grams shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard?

Answer 1