Through process design improvements, the process standard deviation can be reduc

Question

Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. If required, round your answer to four decimal places. Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations. (a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. If required, round your answer to four decimal places. Show me with excel formulas

Explanation / Answer

Ans:

(a) Start with the given +/- 1 standard deviation values = 9.85 and 10.15. Now, find the probability of defects ...

P(X < 9.85) = P[z < (9.85 - 10) / 0.15) = P(z < -1)
From the Standard Normal table ...

P(z < -1) = 0.1587

Since the Normal is perfectly symmetric, P(X > 10.15) = P(z > 1) will also equal 0.1587

So the total probability of defects = 0.1587 + 0.1587 = 0.3174


(b) Number defects in a 1000 unit production = 1000 x 0.3174 = 317 defects

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