Acertain disease has an incidence rate of 0.6%. if the false negative rate is 8% and the false positive rate is 5%, compute the probability that a person who tests positive actually has the disease.

The probability that a person who tests positive actually has the disease is 9.96 %

Step-by-step explanation:

Given:

Rate of incidence of disease is 0.6%. So, 0.6% of the persons have actually a disease.

Percent of persons not having the disease will be 100 - 0.6 = 99.4%

Let the event of having disease be 'D'. Therefore,

False negative rate means that the person having disease shows negative test result.

Let the events 'P' and 'N' represent positive test and negative test results respectively.

As per question,

Also, false positive test result means the person not having disease showing a positive test result. Therefore,

Now, we are asked to determine the probability of a person who tests positive actually has the disease, , which is given using the Bayes' Theorem:

Therefore, the probability that a person who tests positive actually has the disease is 9.96 %

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: