Math 011- MACIO Twelve percent of the job applicants for a large company have wh

Question

Math 011- MACIO Twelve percent of the job applicants for a large company have who have recently smoked marijuana will test positive. the other 2% will test arjma The est negative. The test has The company gives 98% of dose meaning t arijuana, the test will correctly yiea a the ote all applicants a drug test. The sest is not perfect. The test has a sensitivity of of 96%-meaning that if someone has not recently smoked negative test result 96% of the time. Let, M -applicant has recently smoked marijuana C - applicant has not recently smoked marijuana (elean) x positive test (test indicates that the person has smoked marijuana N - negative test (test indicates that the person has not recently smoked recently) marijuana) You may wish to make a tree diagram on scratch paper to help find the proportion smoked recently and test positive, etc. Fill in the proportions in the table and answer the of applicants who have | M1-smoked C-hasn't | | totals recently Smoked X-test is sitive N = test is ive 1.0000 totals Show your answers rounded to four decimal places if rounding is necessary a) What proportion of the applicants get an incorrect test result? a) b) What proportion of the applicants test positive? b) ) What proportion o of those who lest positive have not recently smoked marijuana? d) What proportion of those who pass the drug test really shouldn't have? d)

Explanation / Answer

In the problem it is mention that 12% of the job applicant of the large company have recently smoke marijuana

So figure in the total of M column will be 1000 * 12% = 120

and total in the C column will be 1000 - 120 = 880

98% of those who have recently smoked marijuana will test positive

recent smoke and positive ( Intersection cell of M and X) = 120 * 98% = 117.6

and intersection cell of M and N = 112 - 117.6 = 2.4

96% someone has not recently smoked marijuana, and yield negative test result

It indicate the intersection point of C and N (hasn't smoke and negative test ) = 880 * 96% = 844.8

and in intersection cell C and X = 880 - 844.8 = 35.2

Part a) Incorrect test result

Solution :- We say the test result is incorrect if (recently smoke and test is negative ) + ( hasn't smoked and test is positive)

value of recently smoke and test is negative = 2.4  

Value of hasn't smoked and test is positive = 35.2

Proportional of applicant get incorrect test result = (35.2 + 2.4 ) / 1000 = 37.6 / 1000 = 0.0376

Proportional of applicant get incorrect test result = 0.0376

Part b) What proportion of applicant test positive

Solution :- Consider the total of X row for the positive test

Proportion of positive test = 152.8 / 1000 = 0.1528

Part C) What proportion of those who test positive have not recently smoked manijuana.

Solution :- We will break this statement in 2 parts

1 part :- need to find proportion of those who test positive

So positive test is on X row, total of X row = 152.8

Part 2 :- have not recently smoked manijuana

In row X 35.2 have not smoked manijuana

So the propertion will be 35.2 / 152.8 = 0.2304

Part D) What Proportion of those who pass the drug test really shouldn't have ..?

Solution :- the statement "who pass the drug test really shouldn't have" indicate about the incorrect result, hence already answer in part a) 0.0376

M C Total X 117.6 35.2 152.8 N 2.4 844.8 847.2 Total 120 880 1000

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