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 12 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 11.85 or greater than 12.15 ounces will be classified as defects. What is the probability of a defect (to 4 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 11.85 or greater than 12.15 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)?

c. In a production run of parts, how many defects would be found (to the nearest whole number)?

Explanation / Answer

a) We need to calculate

P(X<11.85)+ P(X>12.15)

= P(Z<(11.85-12)/0.15)+ P(Z>(12.15-12)/0.15)

= P(Z<-1)+P(Z>1)

= 0.3173

b) We need to calculate

P(X<11.85)+ P(X>12.15)

= P(Z<(11.85-12)/0.05)+ P(Z>(12.15-12)/0.05)

= P(Z<-3)+P(Z>3)

= 0.0027

c) If production runs is 1000 parts

No of defect would be = 1000*0.0027 = 3

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.