The problem is \"Twelve percent of the job applicants for a large company have r

Question

The problem is "Twelve percent of the job applicants for a large company have recently smoked marijuana. The company gives all applicants a drug test. The test is not perfect. The test has a sensitivity of 98%- meaning that 98% of those who have recently smoked marijuana will test positive, the other 2% will test negative. The test has a specificity of 96%- meaning that if someone has not recently smoked marijuana, the test will correctly yield a negative test result 96% of the time."

a. What proportion of the applicants get an incorrect test result?

b. What proportion of the applicants test positive?

c. What proportion of those who test positive have not recently smoked marijuana?

d. What proportion of those who pass the drug test really shouldn’t have?

Explanation / Answer

from the above information given we have,

S for smoked, T for tests positive,

P(S) = 0.12,

P(T|S)  = 0.98,

P(~T|~S) = 0.96.

(a) proportion of the applicants get an incorrect test result

=(0.12)*(0.02)*100

=0.24%

(b) proportion of the applicants test positive

=(0.98)*(0.12)*100

=11.76%

(c) proportion of those who test positive have not recently smoked marijuana

=(0.88)*(0.04)*100

=3.52%

(d) proportion of those who test positive have not recently smoked marijuana

=84.48 + 11.76

=96.24%

so. 96.24% of applicants who pass the drug test really shouldn't have .

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