Abby Tudor recently turned 40 years old. Her knees ache, and she often feels short of breath during exercise. She is experiencing fatigue and often feels that she is going in slow motion. Periodic dizziness plagues her during most days. According to the drugstore machine, her blood pressure is elevated. Her family has a history of cardiac disease, with both of her parents having experienced heart attacks. Additionally, an aunt on her mother's side has diabetes. Hypothyroidism also runs throughout her immediate family. Abby is approximately 20 pounds overweight. She has tried various diet and exercise programs in an attempt to lose weight. Her results have been disappointing. With the advice of her physician, she scheduled an appointment for a full physical exam, including a complete blood workup. Her doctor is particularly interested in the level of various blood components that might shed some light on Abby's reported symptoms. Specifically, he wants to examine her white blood cell count, red blood cell count, hemoglobin, and hematocrit figures for indications of infection or anemia. Her serum glucose level will provide information concerning the possibility of the onset of diabetes. Cholesterol and triglyceride levels will provide insight into potential cardiac problems. Additionally, the possibility of hypothyroidism will be investigated by examining Abby's serum TSH level. As instructed, two weeks before her doctor's appointment, she reported to her doctor's lab for a blood test. She confirmed for the lab technician that she had fasted for the 12 hours immediately preceding the exam. During her physical, Abby's doctor went over the blood test report with her. He expressed concern over some of the results, but Abby was not convinced that she had a problem. Additional blood tests were not a viable option because it takes a good deal of time to get a sample of readings and they are expensive. At the time of her doctor's appointment, she was unwilling to accept the offered prescriptions. She chose to do a little research before committing herself to any drug regimen. Her research revealed that many medical measurements, such as cholesterol, are normally distributed in healthy populations. Unfortunately, the lab report did not provide the means and standard deviations necessary for Abby to calculate the various probabilities of interest. However, the report did provide the appropriate reference intervals. Assuming that the reference intervals represent the range of values for each blood component for a healthy adult population, it is possible to estimate the various means and standard deviations for this population. Abby estimated each mean by taking the midpoint of its reference interval. Using the Range Rule of Thumb (s range/4), standard deviations were estimated by dividing the reference interval range by 4. The table on the next page lists Abby's blood test results, as well as the mean and standard deviation for a number of blood test components for the population of normal healthy adults. For any blood component measurement that was below its population mean, Abby decided to calculate the probability that she would get a test value less than or equal to the value obtained, given that she was a member of the healthy population. For example, her HDL cholesterol reading (42 mg/dL) was below the mean of the healthy population (92.5 mg/dL), so she calculated the following probability: P(X ... 42 mg/dL) Similarly, for any blood component measurement reading exceeding its population mean, Abby decided to calculate the probability that she would get a test value greater than or equal to the value obtained, given that she was a member of the healthy population. For example, her LDL cholesterol value (181 mg/dL) exceeds the mean of the healthy population (64.5 mg/dL), so she calculated the following probability:

Abby's Blood Test Component Unit Mean Standard Abby's Result Deviation White blood cell count 103/ UL 7.25 1.625 5.3 Red blood cell count 10/ML 4.85 0.375 4.62 Hemoglobin g/dL 14.75 1.125 14.6 Hematocrit % 43.0 3.5 41.7 Glucose, serum mg/dL 87.0 11.0 95.0 Creatine, serum mg/dL 1.00 0.25 0.8 Sodium, serum mEq/L 141.5 3.25 143.0 Potassium, serum mEq/L 4.5 0.5 5.1 Chloride, serum mEq/L 102.5 3.25 100.0 Carbon dioxide, total mEq/L 26.0 3.0 25.0 Calcium, serum mg/dL 9.55 0.525 10.1 Total cholesterol mg/dL 149.5 24.75 253.0 Triglycerides mg/dL 99.5 49.75 150.0 HDL cholesterol mg/dL 92.5 28.75 42.0 LDL cholesterol mg/dL 64.5 32.25 181.0 LDL/HDL ratio Ratio 1.8 0.72 4.3 TSH, high sensitivity, serum mcIU/mL 2.925 1.2875 3.15 *Population means and standard deviations were estimated from the reference intervals derived from an actual blood test report provided by TA LabCorp, Tampa, Florida. Means were estimated by taking the midpoints of the reference intervals. Standard deviations were estimated by dividing the reference interval ranges by 4. Test results attributed to Abby Tudor are actual results obtained from an anonymous patient