4. HIV/AIDS patients are regularly monitored for their CD4 counts in order to ma

Question

4. HIV/AIDS patients are regularly monitored for their CD4 counts in order to make sure that antiretroviral therapies are effective. Suppose the distribution of CD4 counts in a population is approximately normal with µ=237 and =43. (6 points) A) HIV patients are defined as moving into the AIDS stage of their disease course after their CD4 counts are less than 200. What proportion of patients in this population is suffering from AIDS? B) HIV positive patients maintaining a CD4 count over 350 can frequently carry on regular lives with complications mostly limited to medication side effects. What proportion of patients in this population is considered healthy

Explanation / Answer

Ans:

A)z=(x-mean)/std dev.

P(X<200)

z=(200-237)/43

z=37/43=0.86

P(z<=0.86)=0.8051

Hence,80.51% of the patients are suffereing from AIDS

B)P(X>350)

z=(350-237)/43=2.63

P(z>2.63)=1-P(z<=2.63)=1-0.9957=0.0043

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