A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated that 0.5 % of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the following probabilities:

a. that the test result will be positive
b. that, given a positive result, the person is a sufferer
c. that, given a negative result, the person is a non-sufferer
d. that the person will be misclassified

a) 0.10425

b) 0.00475

c) 0.04975

d) 0

Step-by-step explanation:

a) Pr (the test result will be positive) = (0.95 × ) + ( 0.10 × )

           = 0.00475 + 0.0995

           = 0.10425

b) Pr (positive result, the person is a sufferer) = 0.95 x

           = 0.00475

c) Pr (negative result, non sufferer) = (1-0.95) x

           = 0.04975

d) Pr ( person misclassified) = 0

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this