Manufacture of a certain component requires three different machining operations

Question

Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal distribution, and the three times are independent of one another. The mean values are 20, IS, and 30 min, respectively, and the standard deviations are 1, 2, and 1.9 min, respectively. What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component? (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

THE TOTAL TIME REQUIRE BY THE MACHINE = 20+30+15 = 65

NOW THE TOTAL STANDARD DEVIATION = 1+2+1.9 = 4.9

WE NEED TO FIND P(X<60)

Z = (X-MEAN)/STANDARD DEVIATION

THEREFORE Z = (60-65)/4.9 = -1.02

THEREFORE THE P VALUE FROM Z TABLE = 0.1539

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