Question

The time for a failure to occur in a mechanic arm follows an exponential distribution, typically a failure occurs every 500 hours.

A. What is the probability that the mechanic arm doesn't fail during the first 150 hours?

B. What is the probability of having 2 failures in less than 800 hours?

Answer 1

A. Given it is an exponential distribution,

Fail occurs every 500 hours m = 1/ = 1/500 = 0.002

Probability that mechanical arm doesn't fail for first 150 hours = P(X>150) = 1 - P(X<150) = 1 - (1 - ) = =

  0.74

B. For 2 failures in less than 800 hours, on average one failure takes 500 hours, so the condition left is second failure within 300

hours, P(X<300) = (1 - ) 0.45