Stafford Production, Inc., is concerned with the quality of the parts it purchases that will be used in the end items it assembles. Part number 34-78D is used in the company’s new laser printer. The parts are sensitive to dust and can easily be damaged in shipment even if they are acceptable when they leave the vendor’s plant. In a shipment of four parts, the purchasing agent has assessed the following probability distribution for the number of defective products:
x                 P(x)
0…………….0.20
1…………….0.20
2…………….0.20
3…………….0.20
4…………….0.20
a. What is the expected number of defectives in a shipment of four parts? Discuss what this value really means to Stafford Production, Inc.
b. Compute and interpret the standard deviation of the number of defective parts in a shipment of four.
c. Examine the probabilities as assessed and indicate why this probability distribution might be called a uniform distribution. Provide some reasons why the probabilities might all be equal, as they are in this case.