Roma, a production manager is trying to improve the efficiency of his assembly l

Question

Roma, a production manager is trying to improve the efficiency of his assembly line He knows that the machine is set up correctly only 70% of the time. He also knows that if the machine is set up correctly it will produce good parts 95% of the time, but if setup incorrectly it will produce good parts only 40% of the time. Romi starts the machine and produces one part before he begins the production run He finds the first part to be good. What is the revised probability that the machine was set up correctly 33.5% 12% 66.5 84.7%

Explanation / Answer

Result:

Bayes Theorem used.

C: correctly

NC= Not correctly

G: Produce Good parts

P( C) = 0.70      P( NC)= 0.30

P(G/C) = 0.95     P( G/NC) =0.40

P( C/G) = P(G/C)* P( C) /( P(G/C)* P( C) + P(G/NC)* P(N C) )

=0.95*0.70 / (0.95*0.70+0.40*0.30)

=0.847134

Answer : 84.7%

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