Use the data in the accompanying table, which lists the numbers of correct and w

Question

Use the data in the accompanying table, which lists the numbers of correct and wrong dosage amounts calculated by physicians. In an experiment, two groups of physicians used two different labels for the same amount (concentration label versus ratio label). Show your work.

Answer the following questions.

a) If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose incorrectly?

b) If 2 of the 28 dosage calculations are randomly selected, find the probability that the 2 dosages are both correct and using a concentration label, assuming that the 2 selects are made with replacement.

c) if 2 of the 28 dosages calculations are randomly selected, find the probability that the 2 dosages are both correct and using a concentration label, assuming that the 2 selections are made without replacement.

d) Given that a physican is using a ratio label, what is the probability that the physician is making a wrong decision?

Correct Dosage Calculation Wrong Dosage Calculation Concentration label( 1 milligram in 1 milliliter solution) 11 3 Ratio label (1:1000 solution) 2 12

Explanation / Answer

a) If one of the physicians is randomly selected, the probability of getting one who calculated the dose incorrectly is computed as:

= Number of physicians who calculated the dose incorrectly / Total frequency

= (12 + 3)/ (12 + 3 + 11 + 2)

= 0.5357

Therefore 0.5357 is the required probability here.

b) Probability of getting a correctly measured concentration label = 11 / 28

Therefore, the required probability that 2 dosages are both correct and using a concentration label is computed as:

= (11/28)*(11/28)

= 0.1543

Therefore 0.1543 is the required probability here.

c) Now here we are doing it without replacement, therefore probability here would be computed as:

= (11/28)*(10/27 )

because after drawing one from 11 we would be left with 10

= 0.1455

Therefore 0.1455 is the required probability here.

d) Given that a physican is using a ratio label, the probability that the physician is making a wrong decision

= Physician using a ratio label and making a wrong decision / Physicians using a ratio label

= 12 / (12 + 2)

= 0.8571

Therefore 0.8571 is the required probability here.

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