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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 μ = 7450 and estimated standard deviation σ = 2450. 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? (Round your answer to four decimal places.)
b. Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?
What is the probability of x < 3500? (Round your answer to four decimal places.)
c. Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
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