3) A plant producing silicon wafers for use in integrated circuits inspects each

Question

3) A plant producing silicon wafers for use in integrated circuits inspects each wafer prior to shipping. On average, 12% of the waters are found to be defective and wafer defects occur independently. Suppose that the plant hires one inspector. a) From when the inspector starts work in the morning, on average how many wafers would be inspected before finding one which is defective? b) What is the probability that the sixth wafer inspected will be the first to be defective? c) What is the probability that the tenth wafer inspected is the second to be defective? d) Wafers come to the inspector in lots of 10. What is the probability that at least two of the next four lots contain defective wafers?

Explanation / Answer

D) P(A lot having no defective wafers) = (1 - P(defective wafer)10

= (1 - 0.12)10

= 0.2785

P(having at least 1 defective wafer in a lot) = 1 - 0.2785 = 0.7215

THis is a binomial distribution where P(X) = nCx px qn-x

n = 4

p = 0.7215

q = 0.2785

P(at least 2 of the next four lots contain defective wafers) = P(2) + P(3) + P(4)

= 4C2 x 0.72152 x 0.27852 + 4C1x0.72153x 0.2785 + 4C0x0.72154

= 0.2422 + 0.4184 + 0.2710

= 0.9316

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