Assignment V - ENGM2032 Applied Probability and Statistics...

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ENGM2032, Applied Probability and Statistics Winter 2010 Assignment #5 Due: Monday Feb 15 (Sexton), Tuesday Feb 16 (Studley), 2010 1) There are suspicions that the actual yield strength of steel rods manufactured by a certain company is below the advertised yield strength. After analyzing a sufficient number of rods it has been established that, on average, out of 10 rods, 2 will have yield strengths substantially below the advertised yield strength of 430 MPa, and, therefore, will be considered substandard. Based on this information, a) how many substandard rods is a lot of 100 rods expected to contain? b) what is the probability that a lot of 12 rods contains exactly one substandard rod? c) what is the probability that a lot of 10 rods contains at least two substandard rods? If a large number of rods are inspected one after another, d) how many rods are expected to be inspected before encountering the first substandard one? e) what is the probability that the fifth rod inspected is the first one to be substandard? f) what is the probability that the eleventh rod inspected is the third one to be substandard?
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