Potassium in the blood. Judy’s doctor is concerned that she may suffer from hypo

Question

Potassium in the blood. Judy’s doctor is concerned that she may suffer from hypokalemia (low potassium in the blood). There is variation both in the actual potassium level and in the blood test that measures the level. Judy’s measured potassium level varies according to the Normal distribution with = 3.8 and = 0.2. A patient is classified as hypokalemic of the potassium level is below 3.5

a. If a single potassium measurement is made, what is the probability that Judy is diagnosed as hypokalemic?

b. If measurements are made instead on 4 separate days and the mean result is compared with the criterion 3.5, what is the probability that Judy is diagnosed as hypokalemic?

Explanation / Answer

WILL BE DIAGNOSED WITH HYPOKALEMIC IF X<3.5

MEAN= 3.8

STANDARD DEV = 0.2

A) P(X<3.5) =

For x = 3.5, the z-value z = (3.5 - 3.8) / 0.2 = 1.5

Hence P(x < 3.5) = P(z < 1.5) = [area to the left of 1.5] = 0.0668

B) THE PROBABILITY WILL REMAIN SAME AS THE MEAN OF 4 SEPERATE DAYS WILL NOT BE MUCH DIFFERENT FROM THE MEAN = 3.8

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