Hint(s) Check My Work
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production
process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the
suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.36, and the process control is set at plus or minus one standard deviation. Units with weights less than
9.64 or greater than 10.36 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal
places and for the number of defects to the nearest whole number.
Probability of a defect:
3174
317
Number of defects:
(b) Through process design improvements, the process standard deviation can be reduced to 0.12. Assume that the process control remains the
same, with weights less than 9.64 or greater than 10.36 ounces being classified as defects. If required, round your answer for the
probability of a defect to four decimal places and for the number of defects to the nearest whole number.
Probability of a defect:
0026
Number of defects:
26
(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?
