Question 206282: Hi,
I am really struglling with this question. It's a little tricky. Any help will be much appreciated.
An electronic switching device occasionally malfunctions and may need to be replaced. It is known that the device is satisfactory if it makes, on average no more than .2 errors per hour. A particular five hour period is chosen as a “test” on the device. If no more than 1 error occurs, the device is considered satisfactory. What is the probability that a satisfactory device will be mis-diagnosed as “unsatisfactory” on the basis of the test?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An electronic switching device occasionally malfunctions and may need to be replaced. It is known that the device is satisfactory if it makes, on average no more than .2 errors per hour. A particular five hour period is chosen as a “test” on the device. If no more than 1 error occurs, the device is considered satisfactory. What is the probability that a satisfactory device will be mis-diagnosed as “unsatisfactory” on the basis of the test?
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The device is mis-diagnosed as unsatisfactory if
1. it is a "satisfactory" device
2. it is judged to have failed at least 2 times in five hours.
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P(it is judged to have failed at least 2 times) = 1 -P(0 or 1 failures)
= 0.2627
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Cheers,
Stan H.
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