Question

A statistical process control chart example. Samples of 25 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 25 that require rework. A process problem is suspected if X exceeds its mean by more than three standard deviations Round your answers to four decimal places (a) If the percentage of parts that require rework remains at 1%, what is the probability that X exceeds its mean by more than three standard deviations? Probability0.0258 (b) If the rework percentage increases to 596, what is the probability that X exceeds 1? 0.2642 Probability - (c) If the rework percentage increases to 5%, what is the probability that X exceeds 1 in at least one of the next five hours of samples? 0.8413 Probability

Answer 1

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solution: 6 = 29C1-P) = 25x0.05(1-005) = 1.0897 PCX) =P CX22) = 1- P(O)- P(1) | Cx-9)- |- 0.977 38 - 0301786 PCX 2)- 0 367624 6 35 36 c) probability = 1-PCexceeds in none ofs) 31-01-0.357635 = 10.1094026 -0.8905974 No 8906

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