Assume that a drug test is developed to detect steroid usage by amateur athletes. The test will accurately identify a steroid user 90% of the time. Unfortunately, it will generate a false positive 5% of the time. Assume the test is given to a thousand athletes where it is known that 0.1% are actual steroid users. If an athlete tests positive, what is the probability that he/she actually was using steroids

0.018

Step-by-step explanation:

Probability of (The test will accurately identify a steroid user) = 90% = 0.9

Probability of (generating a false positive(probability of testing positive and he/she is not a steroid user)= 5% = 0.05

Probability of ( actual steroid users) = 0.1% = 0.001

Probability of not been a steroid user = 1 - 0.001 = 0.999

Probability that( he/she actually was using steroid and if an athlete tests positive) = 0.001 × 0.9 / 0.001 × 0.9 + 0.5 × 0.999

= 0.009/0.009 + 0.4995

= 0.009/0.5085

= 0.017699115

Approximately = 0.018

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).