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We use the binomial distribution:
In this formula, <em>c</em> is the acceptable number of defectives; <em>n</em> is the sample size; <em>p</em> is the fraction of defectives in the population. Our <em>c</em> is 2; <em>n</em> is 58; and <em /><em>p</em> is 0.11. Once we evaluate that summation, we get 0.0388. This has a 3.88% chance of being accepted. Since this is such a low chance, we can expect many of the shipments like this to be rejected.
In this formula, <em>c</em> is the acceptable number of defectives; <em>n</em> is the sample size; <em>p</em> is the fraction of defectives in the population. Our <em>c</em> is 2; <em>n</em> is 58; and <em /><em>p</em> is 0.11. Once we evaluate that summation, we get 0.0388. This has a 3.88% chance of being accepted. Since this is such a low chance, we can expect many of the shipments like this to be rejected.