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Health experts’ estimate for the sensitivity of coronavirus tests, as they are actually used, is 0.7....

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Statistics

Health experts’ estimate for the sensitivity of coronavirustests, as they are actually used, is 0.7. They also think thespecificity is very high. Suppose specificity is 0.99 and that thehealth experts’ estimated sensitivity is correct (0.7).

a. In a population where 20% of the population is infected withthe coronavirus, what is the probability that a person who testspositive actually is infected?

b. Continued. What is the probability that a person who testsnegative actually is not infected?

c. If the prevalence of infection in the tested population is0.8 (in other words, if 80% of people tested have the infection),what is the probability that a person who tests positive actuallyis infected?

d. Continued. What is the probability that a person who testsnegative actually is not infected?

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