Question

You work at Little Caesar's, and check the weight of 60 cheese pizzas, discovering a sample Mean of 1446 grams, with sample STDEV of 13 grams. Assume Normality applies.

a. You want to ensure only about 0.74% of the total number cheese pizzas will be out of tolerance for cheese (Failing for too light and too heavy adds up to 0.74%). Where should you set the spec limits?

Answer 1

Solution:

We are given that the condition of normality applies for the given scenario.

We are given

Sample mean = Xbar = 1446

Sample standard deviation = S = 13

Sample size = n = 60

We are given

Both tails area for normal curve = 0.74% = 0.0074

Area at each side = 0.0074/2 = 0.0037

Z score for left side = -2.67829 (by using z-table)

Z score for right side = 2.67829 (by using z-table)

Specification limit = Mean + Z*SD

Lower specification limit = 1446 - 2.67829*13 = 1411.182

Upper specification limit = 1446 + 2.67829*13 = 1480.818

Specification limits should be set at 1411 grams and 1481 grams approximately.