Judy’s doctor is concerned that she may suffer from hypokalemia (low potassium in the blood). Judy’s measured potassium level varies according to the Normal distribution with mean of 3.8 and standard deviation of 0.2 mmol/l. A patient is classified as hypokalemic if the potassium level is below 3.5 mmol/l.
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?
c) What is the potassium level interval (L, U), such that the probability is only 2.5% that the average of 4 measurements is greater than U; and the probability if only 2.5% that the average of 4 measurements is lower than L? e.g., 95% of the sample means fall in the interval.