Statistical Quality Control

ASSIGNMENT #3

1. The content of liquid detergent bottles is being analyzed, twelve bottles, randomly selected from the process, are measured, and the results are as follows (in fluid ounces): 16.05, 16.03, 16.02, 16.04, 16.05, 16.01, 16.02, 16.02, 16.03, 16.01, 16.00, 16.07

(a) Calculate the sample average.

(b) Calculate the sample standard deviation.

2. A lot of size N = 30 contains three nonconforming units. What is the probability that a sample of five units selected at random contains exactly one non- conforming unit? What is the probability that it contains one or more non-conformances?

3. A mechatronic assembly is subjected to a final functional test. Suppose that defects occur at random in these assemblies, and that defects occur according to a Poisson distribution with parameter λ = 0.02

(a) What is the probability that an assembly will have exactly one defect?

(b) What is the probability that an assembly will have one or more defects?

(c) Suppose that you improve the process so that the occurrence rate of defects is cut in half λ = 0.01 to what effect does this have on the probability that an assembly will have one or more defects?

4. A textbook has 500 pages on which typographical errors could occur. Suppose that there are exactly 10 such errors randomly located on those pages. Find the probability that a random selection of 50 pages will contain no errors. Find the probability that 50 randomly selected pages will contain at least two errors.

5. The tensile strength of a metal part is normally distributed with mean 40lb and standard deviation 5 lb. If 50,000 parts are produced, how many would you expect to fail to meet a minimum specification limit of 35lb tensile strength? How many would have a tensile strength in excess of 48lb?