Problem 5.022a The blade and the bearings are important parts of a lathe. The la

Question

Problem 5.022a The blade and the bearings are important parts of a lathe. The lathe can operate only when both of them work properly. For one kind of lathe, the lifetime of the blade is exponentially distributed with the mean three years; the lifetime of the bearings is also exponentially distributed with the mean four years. Assume each lifetime is independent. Round your answer to four decimal places (e.g. 98.7654) What is the probability that the lathe will operate at least three years? Statistical Tables and Charts

Explanation / Answer

P(X > x) = e-x/average

P(late will operate at least 3hours) = P(both blade and bearing operate at least 3 hours)

= P(blade operates at least 3 hours) * P(bearing operates at least 3 hours)

= e-3/3 * e-3/4

= 0.1738

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