You are in charge of the COVID-19 response to results from the rapid antigen testing for Covid-19 that is free to students. Assume the rapid antigen test has a sensitivity of 85% and a specificity of 99%. Assume that the positivity rate for COVID-19 is 3% for students who use a rapid antigen test (i.e., 3% of students who use a rapid antigen test truly have a Covid-19 infection).

For questions 11, 12, 13, and 15 you may want to use Excel or an online calculator for the binomial distribution, such ashttp://stattrek.com/online-calculator/binomial.aspx, to answer the questions.

1. If 100 different students each took a rapid antigen test once during one week, what is the number of students who could potentially have a false positive test?

2. If 100 different students each took a rapid antigen test once during one week, what is the expected number of students who will have a false positive test? Report the number using 2 significant digits. It may not be an integer value.

3. What is the probability that there will be no false positives over 1 week? I.e., what is the probability that no student without COVID-19 will have a positive test over 1 week? Report the probability using 3 significant digits.

4. What is the probability that there will be only 1 false positive over 1 week? I.e., what is the probability that only 1 student without COVID-19 will have a positive test over 1 week? Report the probability using 3 significant digits.

5. What is the probability that there will be 1 or more false positives over 1 week? I.e., what is the probability that 1 or more students without COVID-19 will have a positive test over 1 week? Report the probability using 3 significant digits.