Assume that there is a test for a person having antibodies for COVID-19 disease. Let A denote a test result that shows that a person has antibodies for COVID-19 disease.

Let B denote that a person truly has antibodies for COVID-19. Such a person is thought to be immune to again contracting and spreading COVID-19 because that person already had the disease. (This assumption may or may not be correct, but it does not affect this problem.)

Question 1

Assume that the sensitivity of a test for antibodies is .938 and that the specificity of the test is .956.

In the first column in Excel, create a column for Pr(B) -- this probability denotes the fraction of the general population that has antibodies. The first entry in this column is 0 and increase this value by .01 in successive rows until you reach 1.00. That is, the entries in the first column are 0, .01, .02, .03, ..., .99, 1.00.

In the second column in Excel, use Bayes Theorem to compute Pr(B|A) for all of the rows in the first column.

Use the graphing tool in Excel to create a graph with the first column values on the horizontal axis and the second column values on the vertical axis.

Copy and paste your Excel work into a Word file.

Note: Please provide the word or excel material aswell.