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

a. Here mean is 3.8 and sd is 0.2 as it is mention a patient is classified as hypokalemic if the potassium level is below 3.5. So the probability that Judy is diagnosed as hypokalemic is P(x<3.5)

Converting this in z we have P((x-mean)/sd<(3.5-3.8)/0.2)

=> P(z<-1.5)= 0.0668 (from z table)

b. Here as different samples are used we will use standard error (sd/sqrt(n)) to compute z

Again here also we need to find P(x<3.5).

Converting this into z we get P((x-mean)/(sd/sqrt(n))<((3.5-3.8)/(0.2/sqrt(4)))

=>P(z<-3)=0.0013

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