Chapter 7.5, Problem 16P

Medical: White Blood Cells Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean $\mu =7500$ and estimated standard deviation $$ (see reference in Problem 15). A test result of $x<3500$ is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500?

(b) Suppose a doctor uses the average $\bar{x}$ for two tests taken about a week apart. What can we say about the probability distribution of $\bar{x}$? What is the probability of $x<3500$?

(c) Repeat part (b) for n = 3 tests taken a week apart.

(d) Interpretation Compare your answers to parts (a), (b). and (c). How did the probabilities change as n increased? If a person had $x<3500$ based on three tests, what conclusion would you draw as a doctor or a nurse?