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Normal Distribution - Sheet Metal Stamping Machine

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For the sheet-metal stamping machine in a certain factory, the time between failures, X1 has a mean between the failures, of 56 hours and a variance of 16 hours. The prepair time X2, has a mean time to repair of 5 hours and a variance of 4 hours.

a) If X1 and X2 are independent , find the expected value and the variance of Y=X1+X2, which represents one operation-repair cycle.

b)Would you expect an operation-repair cycle to last more than 75 hours? Why?

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The expert examines sheet metal stamping machines. Clear explanation and solution provided.

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(a) E(Y)= E(X1 + X2) = E(X1) + E(X2) = 56 + 5 = 61

Var(Y)= V(X1 + X2) = V(X1) + V(X2) = 16 + 4 = 20

The operation-repair cycle follows a normal distribution with mean = 61 hrs and SD = ...

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