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Because of natural fluctuations of testosterone in the body, 10 independent blood tests are given to...

Because of natural fluctuations of testosterone in the body, 10 independent blood tests are given to cyclists to test for Performance Enhancing Drugs (PEDs). Those cyclists using PEDs will test positive on any given test with probability 0.85. Those not using PEDs will test positive on any given test with probability 0.15. An overall positive test is defined as testing positive on at least 7 tests of the 10 tests.

a. What is the sensitivity of this test?

b. What is the specificity of this test?

c. Assume that 10% of cyclists are actually using PEDs. If a cyclist tests positive, what is the probability that he is in fact using PEDs

math   Statistics-And-Probability   
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Answer #1

a) sensitivity of this test=P(test positive given taken PEDs)=0.85

b) specificity of this test =P(test negative given not taken PEDs)=1-0.15=0.85

c)

P(tested posiitve)=P(taken PEDs)*P(test positive given taken PEDs)+P(not taken PEDs)*P(test negative given not taken PEDs)=0.1*0.85+(1-0.1)*0.15=0.22

hence probability that he is in fact using PEDs given tested posiitve)

=P(taken PEDs)*P(test positive given taken PEDs)/P(tested posiitve)

=0.1*0.85/0.22=0.3864

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