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21 votes
21 votes
The amount of flight time between failures of an airplane engine is exponentially distributed with mean 900 hours. If the engine is inspected every 600 hours of flight time, what is the probability that the engine will fail before it is inspected

User Pawel Gorczynski
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1 Answer

11 votes
11 votes

Answer:

0.4866 = 48.66% probability that the engine will fail before it is inspected

Explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:


image

In which
image is the decay parameter.

The probability that x is lower or equal to a is given by:


image

Which has the following solution:


image

The probability of finding a value higher than x is:


image

Exponentially distributed with mean 900 hours.

This means that
image

If the engine is inspected every 600 hours of flight time, what is the probability that the engine will fail before it is inspected?

This is
image, which is:


image

0.4866 = 48.66% probability that the engine will fail before it is inspected

User Cyril Mottier
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3.1k points