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The number of defectives in the sample is a random variable which follows a Binomial distribution with parameters and .
The probability of defectives is given as,
The probability of type 1 error.
From definition, probability of type 1 error is he probability of rejecting when it is true. So, and we find the probability of 7 or 8 defectives.
So, when the number of defectives is 7, its probability is, and when the number of defectives is 8, its probability is,
The probability of committing type 1 error is 0.00008192+0.00000256=0.00008448
The probability of type 2 error.
From definition, type 2 error is the probability of accepting when is true. So we determine the probability of 6 or less defectives when .
Therefore, the probability of committing type 2 error is 0.99999927