Question

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces.

(a)

The process standard deviation is 0.09, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.91 or greater than 10.09 ounces will be classified as defects. (Round your answer to the nearest integer.)

Calculate the probability of a defect. (Round your answer to four decimal places.)

Calculate the expected number of defects for a 1,000-unit production run. (Round your answer to the nearest integer.)

defects

(b)

Through process design improvements, the process standard deviation can be reduced to 0.03. Assume the process control remains the same, with weights less than 9.91 or greater than 10.09 ounces being classified as defects.

Calculate the probability of a defect. (Round your answer to four decimal places.)

Calculate the expected number of defects for a 1,000-unit production run. (Round your answer to the nearest integer.)

defects

(c)

What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

Reducing the process standard deviation causes a substantial increase in the number of defects.Reducing the process standard deviation causes a substantial reduction in the number of defects.    Reducing the process standard deviation causes no change in the number of defects.

Answer 1