Question

An FDA regulation controlling the contents of packaged food items states that no more than 5 percent of the items produced and sold can contain less than 95 percent of the stated/labeled weight. Assuming that the standard deviation of the process, when in control or is operating as expected, is 0.90, determine if Siders Breakfast Foods, Inc., is in compliance or not in compliance with the FDA regulation given these parameters, i.e. process mean of 24 ounces and standard deviation of 0.90. Explain and show evidence supporting your conclusion.

What should Siders Breakfast do if they discover their process to be in violation of the Federal regulation?

(Assume that the content weight follows the normal distribution).

Answer 1

Process mean = 24 ounces

Standard deviation = 0.90 ounces

95 percent of labeled weight = 24*0.95 = 22.8 ounces

z value = (22.8-24)/0.90 = -1.33

F(z) = NORMSDIST(-1.33) = 0.0917

This means 9.17% of the items produced and sold contain less than 22.8 ounces or 95% of the labelled weight.

Therefore, Siders Breakfast's process is in violation of Federal regulation.

They should reduce the process variation (standard deviation) in order to reduce the percentage of items having less than 95 per cent of the labelled weight.

For 5% target, z value = NORMSINV(0.05) = -1.645

Target standard deviation = (22.8-24)/(-1.645) = 0.72 ounces

Standard deviation should not be more than 0.72 ounces