Some states have recently initiated programs to randomly test high school athlet

Question

Some states have recently initiated programs to randomly test high school athletes for possible use of anabolic steroids after concerns arose about the health of the athletes and fairness in the sports. Critics of the programs say that the amount of money spent on testing isn’t worth it, since only 1 in 2000 high school athletes actually use steroids to enhance their performance. The test used does have a 97.3% chance of being positive when an athlete uses steroids and a 98.4% chance of showing a negative result when an athlete is not using steroids.

(b) (8 points) An athlete tests positive. What is the chance that he really is using steroids?

(c) (8 points) 10000 athletes are randomly chosen to be tested statewide.

(i) (4 points) What is the expected number of those 10,000 who will test positive?

(ii) (4 points) What is the expected number of those 10,000 who are actually using steroids?

Explanation / Answer

b)

Let

U = using steroids
P = positive

As

P(P) = P(U) P(P|U) + P(U') P(P|U') = (1/2000)*0.973 + (1-1/2000)*(1-0.984) = 0.0164785

Hence,

P(U|P) = P(U) P(P|U) / P(P)

= (1/2000)*(0.973)/0.0164785 = 0.029523318 [ANSWER]

***********************

c)

i)

E(positive) = 0.0164785*10000 = 164.785 [ANSWER]

ii)

E(using) = (1/2000)*10000 = 5 [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.