eBook {Exercise 6.35 Algorithmic} Motorola used the normal distribution to deter

Question

eBook {Exercise 6.35 Algorithmic} 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 14 ounces. a. The process standard deviation is 0.15, and the process control is set at plus or minus 1 standard deviation . Units with weights less than 13.85 or greater than 14.15 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 (round to the nearest whole number)? 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 13.85 or greater than 14.15 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)? In a production run of 1000 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? |- Select your answer -

Explanation / Answer

a)probability of defect =1-P(13.85<X<14.15)=1-P(-1<Z<1)=1-0.6827 =0.3173

for a production run of 1000 ; defects =np=1000*0.3173 ~ 32

b)

probability of defect =1-P(13.85<X<14.15)=1-P((13.85-14)/0.05<Z<(14.15-14)/0.05)=1-P(-3<Z<3)=1-0.9973=0.0027

for a production run of 1000 ; defects =np=1000*0.0027 =~3

c) reducing number of defects

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