In pharmacologic research, a variety of clinical chemistry measurements are routinely monitored closely for evidence of side effects of the medication under study. Suppose for adults, typical blood-glucose levels are normally distributed with mean 90 mg/dL and standard deviation 38 mg/dL. Suppose the normal range is 65 to 120 mg/dL.
In some studies, only values at least 1.5 times as high as the upper limit of normal are identified as abnormal. Frequently, tests that yield abnormal results are repeated for confirmation. What is the probability that for a normal person, a test will be at least 1.5 times as high as the upper limit of normal on two separate occasions? Assume the test results are independent.