Cholesterol levels in psychiatric patients. A study of serum cholesterol levels in psychiatric patients of a maximum-security forensic hospital revealed that cholesterol level is approximately normally distributed with a mean of 208 milligrams per deciliter (mg/dL) and a standard deviation of 25mg/dL. (Journal of Behavioral Medicine, Feb. 1995.) Prior research has shown that patients who exhibit violent behavior have cholesterol levels below 200 mg/dL.
a. What is the probability of observing a psychiatric patient with a cholesterol level below 200 mg/dL?
b. For three randomly selected patients, what is the probability that at least one will have a cholesterol level below 200 mg/dL?
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