A certain blood test accurately indicates the presence of a disease 87% of the time when the disease is actually present. The test indicates the presence of the disease 0.4% of the time when the disease is not present. If 2% of the population has the disease, what percentage of the total population will receive a false positive

Question

Mathematics

Chiquita

7 May, 06:30

A certain blood test accurately indicates the presence of a disease 87% of the time when the disease is actually present. The test indicates the presence of the disease 0.4% of the time when the disease is not present. If 2% of the population has the disease, what percentage of the total population will receive a false positive

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Answers (1)

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Emilie Harper · Answer 1

0.392% of the total population will receive a false positive

Step-by-step explanation:

We have that:

2% of the population has the disease.

So 100-2 = 98% of the population does not have the disease.

For 0.4% of the people who do not have the disease, the test is positive.

What percentage of the total population will receive a false positive

0.4% of 98%. So

0.004*0.98 = 0.00392

0.392% of the total population will receive a false positive