Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then ( ( 7500 and ( ( 1750 (Reference: Diagnostic Tests with Nursing Applications, S. Loeb).

A random sample of n = 50 workers from the toxic cleanup site were given a blood test that showed x̅ = 6820. What is the probability that, for healthy adults, x̅ will be this low or lower?

(a) How does the central limit theorem apply? Explain.

(b) Compute P(x̅ ( 6820).

(c) Interpretation Based on your answer to part (b), would you recommend that additional facts be obtained, or would you recommend that the workers' concerns be dismissed? Explain.