Judys doctor is concerned that she may suffer from hypokalem

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 p = 3.8 and o = 0.2. A patient is classified as hypokalemic if the potassium level is below 3.5. If a single measurement is made, what is the probability that Judy is diagnosed as hypokalemic (Sentence)? 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 (Sentence)?

Solution

A) If a single potassium measurement is made, what is the probability that Judy is diagnosed as hypokalemic? P(X<3.5)=P((X-mean)/s <(3.5-3.8)/0.2) =P(Z<-1.5) =0.0668 (check standard normal table)