Question: Some of the ideas of the normal probability distribution are relevant to the characterization of laboratory tests. Suppose that albumin has a normal distribution in a healthy population with mean \(\mu \) = 3.75 mg/dl and \(\sigma \) =0.50 mg/dl. The "normal" range of values will be defined as \(\mu \pm 1.96\sigma \), so that values outside this interval will be classified as "abnormal". Patients with advanced chronic liver disease have reduced albumin levels that are also normally distributed. Suppose that, in this population, the mean is u = 2.5 mg/dl and a = 0.50 mg/dl.

1. In evaluating results for a single patient, what values of albumin will lead to a classification of "abnormal"?
2. What proportion of patients in the population with advanced chronic liver disease will have values of albumin that will lean to an incorrect classification of "normal"?
3. If a single patient with advanced chronic liver disease is tested, what is the probability that s/he will be correctly classified?

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