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 ounces. a. The process standard deviation is , and the process control is set at plus or minus standard deviation . Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of parts, how many defects would be found (round to the nearest whole number)? b. Through process design improvements, the process standard deviation can be reduced to . Assume the process control remains the same, with weights less than or greater than ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)? In a production run of parts, how many defects would be found (to the nearest whole number)? c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean? Hide Feedback Incorrect Check My Work Icon Key Previous Question 12 of 16 Next Exercise 06.35 Algorithmic

Explanation / Answer

a)probability of a defect =p(z>1)+p(z<-1)=0.3173

b)defects would be found in 1000=1000*0.3173=317.3

so defects=317

c)probability of a defect =p(z>7.15-7/0.05)+p(z<6.85-7/0.05)=p(z>3)+p(z<-3)=0.0027

d)defects in 1000=1000*0.0027=2.7

defects=3

e)What is the advantage of reducing process variation?

A. It can substantially reduce the number of defects

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