Question

Problem 3: [4 points) Manufacture of a certain component requires three different machining operations. Machining time for each operation is normally distributed and the three times are independent of one another. The mean values are 15, 30, and 20 minutes respectively. Their standard deviations are 1, 2, and 1.5 minutes respectively. What is the probability that it takes at least 1.5 hour of machining time to produce a randomly selected item?

Answer 1

X, X2, X3 these Let three different machining hining operations are given that x, ~ Nlis,is , & ₂ ~N 130, 2), X₂ ~N 130,2²), xg~ 120, 1.5² - manufacture of a certain component requires all machining operations ~N165, 7.25) Required probability P(x, +X2 + X₂ > 1.5860) [..s 1. snown = 1.5x60 min) :p ( x, +X2 + X3 > go) Hence x + x2 + x3 90-6S Plz > = P(Z > 9.29) = 0 (from table 17.25. . Required probability :