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 μ = 3.75 mg/dl and σ = 0.50 mg/dl. The “normal” range of values will be defined as μ + 1.96 σ, 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 μ = 2.5 mg/dl and σ = 0.50 mg/dl.

If a single patient with advanced chronic liver disease is tested, what is the probability that she will be correctly classified?