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We've seen binomial distributions used in a few contexts so far, but there are many more situations where the binomial model applies. One example involves

We've seen binomial distributions used in a few contexts so far, but there are many more situations where the binomial model applies. One example involves testing sensitivity and specificity for medical tests. The sensitivity of a test is the true positive rate. In other words, the sensitivity is the probability that a person with the condition is correctly identified as having it. The specificity of a test is the true negative rate. In other words, the specificity is the probability that a person without the condition is correctly identified as not having it. We'll consider these ideas in the context of rapid strep tests. Rapid strep tests are useful because the standard way to test for strep throat is to take a throat culture, which can take a few days to come back. If the rapid test comes back positive, the patient can get started on treatment right away and get better more quickly. If the test comes back negative but the physician is still concerned the patient might have strep, they will sometimes call for the throat culture at that point. On average, rapid strep tests have been found to have 86 % sensitivity and 95 % specificity.1

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