A research group is working to create a better test for screening of a particular disease. The current gold- standard has a sensitivity of 90% and a specificity of 80%. Data from 2019 estimated that the current prevalence of the disease is 2.7% of the population. (a) (4 pts) What is the probability a person is not infected with the disease if the test comes back negative? (b) (3 pts) The scientists believe they can increase both the sensitivity and specificity of the test to 95%. In this new scenario, what is the probability a person is not infected with the disease if the test comes back negative? (c) (3 pts) The scientists collect new patient data and distressingly find that the estimated probability of an individual not being infected with the disease given that they tested negative has not improved on the gold-standard test. The scientists are convinced their clinical data correctly measured the sensitivity and specificity to be 95%. What could have happened?