1 Citing recent evidence that HIV infections are best managed when treated early

Question

1 Citing recent evidence that HIV infections are best managed when treated early, an influential panel of medical experts has finalized its recommendation that all people ages 15 to 65 be screened for the virus that causes AIDS. The recommendation from the U.S. Preventive Services Task Force seeks to address one of the key challenges in the fight against HIV/AIDS: The window during which patients respond best to treatment is also the time when symptoms of the disease are least noticeable. Let us say that an HIV test correctly returns a positive result (person has HIV) 96% of the time.

1 If forty people with HIV are given this test, what is the expected number of positive results? Write out the exact answer you get, don't round.  

2 If forty people with HIV are given this test, what is the standard deviation number of positive results? Round to the nearest hundredths place. ________

3 If forty people with HIV are given this test, what is the probability of seeing 35 results or less come back positive? Round your answer to the ten-thousandths place.

Explanation / Answer

If forty people with HIV are given this test, what is the expected number of positive results? Write out the exact answer you get, don't round.  

1 .0.96*40 = 38.4

2. (0.96*0.04*40)^0.5 =1.24

3.Z = (M - ) / (2 / n)

Z = (35 - 38.4) / (1.5376 / 40)

Z = -3.4 / 0.19606

Z = -17.34152

P(X<35) = 0

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