Motorola used the normal distribution to determine the probability of defects an

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 7 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 6.85 or greater than 7.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found (to 0 decimals)? b.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 6.85 or greater than 7.15 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)? In a production run of 1000 parts, how many defects would be found (to 0 decimals)?

Explanation / Answer

a)

hence probability of a defect =1-0.8664 =0.1336

expected defects =np=1000*0.1336 =133.6 ~ 134

b)

for std deviation =0.05

hence probability of a defect =1-0.9973 =0.0027

expected defects =np=1000*0.0227 =2.7~ 3

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