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In: Statistics and Probability

The optimal scheduling of preventative maintenance tests of some (but not all) of n independently operating...

The optimal scheduling of preventative maintenance tests of some (but not all) of n independently operating components was developed. The time (in hours) between failures of a component was approximated by an exponentially distributed random variable with mean 1300 hours. [Round to 4 decimal places where necessary.]

1. Find the probability that the time between a component failures ranges is at least 1600 hours.
2. Find the probability that the time between a component failures ranges between 1600 and 1900 hours.

3. Suppose a component is still working after 1600 hours, find the conditional probability that it will fail before 1900 hours.

4. If 9 components are tested, find the probability that at least 2 of them failed between 1600 and 1900 hours

5. Suppose 9 components are tested. What is the probability that 2 of them failed between 1600 and 1900 hours?


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orchestra answered 2 years ago
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