5. Assume the likliehood function of the negative tests is a Gaussian centered at 3 with a standard deviation of 1.5 and the likliehood function of the positive tests is a Gaussian centered at 6 with a standard deviation of 2. If we want to have a false positive rate of only 2%, what should the cutoff value be? What will be the false negative value for this choice of the cutoff? Table 1: Assay Clinical Study Results RT-PCR Method Subtotal Positive Negative IgG+/gM+ 78 78 COVID-19 IaG/gM Positive IgG-/gM+ 1 1 Rapid Test IgG+/igM- 9 11 Cassette Negative IgG-/gM- 3 101 Subtotal 90 101 191 IgG Positive Percent agreement (PPA): 96.7% (87/90) (95%CI: 90.7%-98.9%) Negative Percent agreement (NPA): 98.0% (99/101) (95% Ci: 93.1%%-99.5%) IgM Positive Percent agreement (PPA): 86.7%% (78/90) (95%CI: 78.1%-92 2%) Negative Percent agreement (NPA): 99.0% (100/101) (95%CI: 94.6%-99.8%) Overall (either IgG+ or IgM+) Positive Percent agreement (PPA): 96.7%% (87/90) (95%CI: 90.7% -98.9%) Negative Percent agreement (NPA): 97.0 (98/101) (95%CI: 91.6%-99.0%)