Question

A machine fills 24-ounce (according to the label) boxes with cereal. The amount deposited

into the box is normally distributed with a standard deviation of 0.25 ounce. What does the
mean have to be in order for 99.5% of the boxes to contain 24 ounces or more of cereal?

Answer 1

Answer: We do not know the mean  but we do know the standard deviation which is 0.25 ounces. The normal distribution plot below shows the shaded

region at approximately 5% of the area of the total Gaussian distribution.

From a Table we find that 5% is a z = -2.57 and so the mean must be 2.57

multiplied by 0.25 ounces = 3.57  0.25 = 0.643 ounces. The mean value

of box must be 0.643 ounces above the declared 24 ounces. Thus,

Mean value =  = 24.643 ounces

Explanation: