ISEN 3710 Engineering Statistics 1. A production manager has data on three machi

Question

ISEN 3710 Engineering Statistics 1. A production manager has data on three machines A, B, and c that indicates 9 out of 1000 parts from machine A, 16 out of 2000 parts from machine B, and 15 out of 1500 parts from machine C are defective. a.) What is the conditional probability of "a defect, given, it came from machine c, i.eP(DIC)? b.)If an assembler that has received 258, 358, and 408 of his parts from machines A, B, and C, respectively, what is the probability that, upon discovery of a defective part, it came from machine B, i.e.. P(BID)? 2. It is known that the average weight of parcels conforming to certain outside dimensions is 90 lbs. with a variance of 40 lbs. What is the probability of a conforming parcels being more than 100 1bs.? 3. A certain product is received in lots of 1000 units. The quality control acceptance procedure is to choose 50 units at random from the lot and test them. If zero or one units in the sample are found defective the entire lot is rectsied (bad parts are replaced with known good parts) a accepted. What is the probability that a lot containing5 defective parts will be accepted? Solve using the binomial distribution approximation to the hypergeometric distribution. . The number of calls per minute arriving at a telephone switchboard may be randomly distributed according to a poisson distribution. If an average of 500 calls per hour arrive at a switchboard, what is the probability that no more than 10 calls will arrive during any given minute?

Explanation / Answer

Question 1 (A) Here P(D l C) = Number of defects/ Number of parts from machine C = 15/1500 = 0.01

(B) Here

P(B l D) = Pr(D l B) * Pr(B) / [ Pr(D l A) * Pr(A) + Pr(D l B) * Pr(B) + Pr(D l C) * Pr(C) ]

P(B l D) = (16/2000) * 0.35 / (9 /1000 * 0.25 + 16/2000 * 0.35 + 15/1500 * 0.40)= 0.3094

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