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Np and n1 p represent the expected number of successes

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Unformatted text preview: that whenever np and n(1 – p) are each at least 10, we consider a sampling distribution of sample proportions to be approximately normal. np and n(1 – p) represent the expected number of successes, and the expected number of failures, respectively, in the sample. A success indicates that an event occurred in a sample and a failure indicates that an event did not occur in a sample. Since p is generally unknown, we must find alternative criteria for normality. Rather than finding the expected number of successes and failures in the sample, we instead determine the actual number of successes and failures in the sample. The actual number of successes in the sample is !!, and the actual number of failures is !(1 − !). If these are each at least 10, we will consider the criteria for approximate normality to be satisfied. The actual num...
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