Student S has a flu 20% the time. Suppose we can only detect whether he has flu or not by his body temperature, which is a continuous random variable. Without flu, the temperature of a person is N ~ (98.6, 0.4) With flu, the body temperature of a person is N ~ (101,2) If S’s body temperature today is 100, what is the probability that he has the flu?
I have tried to solve it this way: $Z_Nflu$ = $ {(X-98.6)/ 0.6}$
$Z_flu$ = $(X-101/ 1.4)$
P($Z_flu$ = 100) = (-0.71) = 1- 0.76 = 0.24
P(flu | temp) = (0.24* 0.2) /(0.2 * 0.24 + 0.8 *0.99)
Is this correct?
Should not it be P(flu | temp) = (0.99* 0.2) /(0.2 * 0.24 + 0.8 *0.99), since we need to find the probability of temperature 100 belonging to with flu temperature data set ?