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Problem # 50

Problem # 50. Dr. Ali Moshtagh Probability Problems. The Michigan Molding Co.

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Problem # 50

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  1. Problem # 50 Dr. Ali Moshtagh Probability Problems

  2. The Michigan Molding Co. The Michigan Molding Co. produces two-color legend plates for aircraft cockpits using four machines ( W, X, Y, and Z ). After quality-control inspection, the plates are graded as A, acceptable; B, needs repair; and C, can be scrapped. 1

  3. A sample of 1,000 legend plates revealed the following results: 2

  4. State in symbols, the probability that a legend plate selected at random • was produced by machine W. • was produced by machine X and needs repair. • Needs repair given that it was produced by machine Y. • (restricted to plates produced by machine W) is acceptable. • was either produced by machine Z or can be scrapped. 3

  5. State in words the meaning of each of the following • P ( B | Z ) • P ( A  Y ) • P ( B U X ) 4

  6. Compute the probability that a plate selected at random • was produced by machine Z. • was produced by machine X and is acceptable. • is acceptable, given that it was produced by machine X. • is either in need of repair or was produced by machine W. 5

  7. Use the addition theorem or multiplication theorem, as appropriate, to compute the following probabilities • P ( Y  B ) • P ( C U X ) • P ( A  C ) 6

  8. Determine if the variables (machine and grade) are statistically independent and show why or why not. 7

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