# Normal Distribution - Sheet Metal Stamping Machine

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?

© BrainMass Inc. brainmass.com June 3, 2020, 9:20 pm ad1c9bdddfhttps://brainmass.com/statistics/normal-distribution/normal-distribution-sheet-metal-stamping-machine-177745

#### Solution Preview

(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 = ...

#### Solution Summary

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

$2.19