Two types of flaws may occur during the fabrication of steel beams: (1) the inclusions of...

Two types of flaws may occur during the fabrication of steel beams: (1) the inclusions of small quantity of foreign matter “slag”; and (2) the existence of microscopic cracks. It has been found by careful laboratory investigation that for a certain size I-beam from a given fabricator, the mean distance between microscopic cracks is 40 feet along the beam, whereas the slag inclusions exist with an average rate of four (4) per 100 ft. of the beam. Each of these types of flaws follow a Poisson process.

a) For a 20-ft I-beam, what is the chance of finding exactly two microscopic cracks in the beam?

b) For the beam in a, what is the probability of finding one or more slag inclusions?

c) If a 20-ft beam contained more than two flaws, it would be rejected. What is the probability of rejecting a 20-ft beam?

d) Four 20-ft beams were supplied to a contractor by this fabricator last year. Assume that the flaw conditions among the four beams are statistically independent. What is the probability that only one beam had been rejected?

Expert Solution

Ally Wells answered 2 years ago

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