Question 1 options: Nova has a pop quiz with 9 multiple choice questions. Each question has 3 answer options. Assume that Nova randomly guesses on every question. Find the probability that Nova passes the test with a score of 70% or more. Round to the nearest tenth of a percent (1 decimal place percent).
Question 2
Question 3
The sensitivity of a medical 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.
Let's suppose we are dealing with a rapid strep test with 86% sensitivity and 95% specificity. 86% sensitivity means that of the people who actually have strep, 86% will test positive. This means that 14% of the people who actually have strep will test negative; these are called false negatives. A false negative can lead to a patient delaying the antibiotic treatment they need.
Question 3
Suppose we take a random sample of 30 people who have strep throat and are tested with this rapid strep test. Let X be the number of people who receive false negatives. Since we will not be sampling with replacement, assume that we are sampling from a population that is large enough so that the probability of success is close enough to the same in each trial that the sampling can be considered independent.
Question 3 (1 point)
Question 4
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