Question: Medical: White Blood Cells Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood. Assume that x has a distribution that has approx. normal with mean µ = 7500 and estimated standard deviation σ = 1750. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be a result of a viral infection.

1. What is the probability that on a single test x is less than 3500?
2. Suppose that 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?
3. Repeat part (b) for n = 3 tests taken a week apart.
4. Compare your answers for parts (a), (b), and (c). how did the probabilities change as n increased? If a person had \(\bar{X}\) < 3500 based on three tests, what conclusion would you draw as a doctor or nurse?

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