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An application communicating with a database started to fail with network errors. The errors occur only during some runs, and at random times when running the application. If a network error occurs, the application will fail and exit immediately. During the past week, the application succeeded 23 times and failed 7 times.

As a workaround, until the network error has been identified and fixed, the application has been moved to a new environment. It is still communicating with the same database. We need to test, if the error is gone in the new environment.

Question: based on the previous observations of 23/7 successful/unsuccessful runs, how many successful consecutive runs N must be observed to be able to say with X % confidence, that the error is gone?

For example, to be able to say with 99.9 % confidence that the error is gone, the application must produce N consecutive successful runs.

How to compute N?

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