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 13 ounces.
a) The process standard deviation is 0.1, and the process control is set at plus or minus 1.5 standard deviations. Units with weights less than 12.85 or greater than 13.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?
b) In a production run of 1000 parts, how many defects would be found (to 0 decimals)?
c) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same, with weights less than 12.85 or greater than 13.15 ounces being classified as defects. What is the probability of a defect (rounded to 4 decimals; getting the exact answer, although not necessary, will require Excel)?
d) In a production run of 1000 parts, how many defects would be found (to 0 decimals)?