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 6 ounces. a. The process standard deviation is 0.10 , and the process control is set at plus or minus 1.75 standard deviation s. Units with weights less than 5.825 or greater than 6.175 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 0.06 . Assume the process control remains the same, with weights less than 5.825 or greater than 6.175 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?

Explanation / Answer

Answer to the question)
Part a)

Mean M = 6

Standard deviation S = 0.10

Z1 = -1.75

Z2 = +1.75

P(defect)= P(z < -1.75) + P(z > +1.75)

P(z < -1.75) = 0.040059 .......[refer to the z table]

P(z > +1.75) = 1 - 0.959941 = 0.040059

P(defect ) = 0.040059 + 0.040059 = 0.0801

If n = 1000 , number of defects = 1000*0.0801 = 80.1 ~ 80 parts

.

Part b)

S = 0.06

P(defect) = P(x < 5.825) + P( x> 6.175)

P(x < 5.825) = (5.825-6) / 0.06 = -2.92

P(z < -2.92) = 0.00175

P(x > 6.175) = (6.175-6)/0.06 = 2.92

P(z > 2.92) = 1 - 0.99825 = 0.00175

P(defect) = 0.00175 +0.00175 = 0.0035

For n = 1000 , number of defects = 1000*0.0035 = 3.5 ~ 4 units

.

Part c)

By reducing the process variation , we got more consistent production of units , leading to lesser number of defects , and providing more profitable production process

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