Question: 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 \(\sigma \) = 1750 (see reference in Problem 7). A test result of X < 3500 is an indication of leucopoenia. This indicates bone marrow depression that may be the result of a viral infection.

1. 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 \(\bar{X}\) < 3500?

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

(d) Compare your answers for parts (a), (b), and (c). How did the probabilities change as n increased? If a person had a test result of \(\bar{X}\) < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document