The prevalence of diabetes in the U.S. was reported to be 9.3% in 2012. Suppose a...

The prevalence of diabetes in the U.S. was reported to be 9.3% in 2012. Suppose a certain locality had a population of 100,000 people. If this locality was no different from the entire U.S. population, we expect to find 9.3%(100,000) = 9,300 people with diabetes. Suppose a sample of size 1,000 was randomly chosen without replacement from this locality. Let X is the number of individuals in the sample with the disease. (a) Write the pdf of X. Report the mean and standard deviation of X. (b) It was found that out of the 1,000 people, 114 had diabetes, not exactly 93. Calculate P[X ≥ 114]. (c) X has a hypergeometric distribution because the sampling was done without replacement. Suppose the sampling was done with replacement. If Y is the number of individuals that had diabetes in the sample of size 1,000, then Y ∼ Bin(n = 1, 000, p = 0.093) Write the pdf of Y . Also, report the mean and standard deviation of Y . (d) It was found that 114 people had diabetes, not exactly 93. Find P[Y ≥ 114]. (e) Compare the probabilities in Question 12b and 12d. Did you expect the probabilities to be similar in value? Why or why not?

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Expert Solution

here for obtaining cumulative probability X less than or equal to 114, individual probabilities from 0 to 114 are computed for geometric distribution and added in excel.

orchestra answered 1 year ago

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