Specification Limits & Distribution Analysis in a Candy Factory

Scenario: You are the Operations Manager for a candy manufacturing company. The Marketing Department has printed new labels for your 1-pound (16 oz) bags of jelly beans. Internal quality standards state that each bag can weigh 1%<16oz.<2.0% with a standard deviation of 0.186 ounces. You take a 100 bag random sample from your process (25 subgroups of 4 bags) and weigh each bag; the mean weight was 16.00 ounces. The total range of the 25 subgroups is 87.5 ounces. The 100 bag sample contains 30 bags of yellow jellybeans, 25 bags of orange jellybeans, 20 bags of red jellybeans, 15 bags of green jellybeans and 10 bags of black jellybeans. Using these data answer the following.

1. Calculate the (USL&LSL) specification limits in ounces (16 oz. +2.0%; 16 oz.-1.0%)

2. Sketch a rough drawing of the distribution curve showing the mean and specification limits (4 points).

3. What are the Z values for the USL & LSL?

4. What is the area beyond the USL & LSL independently?

5. What is the statistical probability of reaching into the container that holds this sample of 100 bags of jellybeans and pulling out 1 bag of jellybeans weighing less than 15.49 ounces?

6. If you were to reach into the container that holds this sample of 100 bags of jellybeans and randomly pull out two bags of jellybeans, what is the statistical probability that both bags of jellybeans (after replacing the first) weighed more than 16.00 ounces (assume the weights are normally distributed)?

7. If you were to reach into the container that holds this sample of 100 bags of jellybeans and randomly pull out two bags of jellybeans, what is the statistical probability that one bag will weigh less than 16.00 ounces and the other bag weighs more than 16 ounces? Assume that you do not replace the first bag and the weights are normally distributed.