Abby Tudor recently turned 40. Her knees ache and she feels shortness of breath during exercise, along with periodic dizziness and general fatigue. Despite trying various diet and exercise regimes, Abby is 20 pounds overweight. According to a drugstore machine, her blood pressure is elevated. Her family history includes cardiac disease (both parents had heart attacks), diabetes (a maternal aunt), and hypothyroidism (throughout immediate family). Her physician advised scheduling an appointment for a full physical exam and complete blood work, hoping levels of various blood components may clarify Abby's symptoms. He is interested in her white and red blood cell counts, hemoglobin, and hematocrit figures for indications of infection or anemia. Additionally, he will test serum glucose levels for the onset of diabetes, cholesterol and triglyceride levels for potential cardiac disease, and serum TSH levels for the possibility of hypothyroidism. Two weeks before her appointment, Abby fasted for 12 hours and immediately had blood work done at the lab. At her physical, the doctor reviewed her blood test report. He expressed concern over some results but Abby wasn't convinced she had a problem. Additional blood tests weren't an option because of the expense and amount of time they take. Abby decided to forego the offered prescriptions at that time and do some research herself. She found that many medical measurements, such as cholesterol, are normally distributed in healthy populations. While her lab report did not provide the means and standard deviations needed to calculate the various probabilities of interest, it did provide the appropriate reference intervals. Assuming 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, standard deviations were estimated by dividing the reference interval range by 4 (σ ≈ range/4). The table below shows 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) with μ = 92.5 and σ = 28.75. Similarly, for any blood

1. The reference interval for HDL cholesterol is 35-150 mg/dL. Use this information to confirm the mean and standard deviation provided for this blood component. 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: P(X ≥ 181 mg/dL2. To help her interpret the calculated probabilities, Abby decided to only focus on blood components that had a probability of less than 0.025. By choosing this figure, she acknowledged that it is unlikely she could have such an extreme blood component reading and still be part of the healthy population.
2. Using Abby's criteria and the means and standard deviations provided in her blood test report, determine which blood components should be a cause of concern for Abby. Write up a summary report of your findings. Be sure to include a discussion concerning your assumptions and any limitations to your conclusions.

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Blood Test Components for Healthy Adults and Results for Abby Tudor* Blood Component Unit Mean Standard Abby's Result Deviation 10/µL 10/µL White blood cell count 7.25 1.625 5.3 Red blood cell count 4.85 0.375 4.62 Hemoglobin g/dL 14.75 1.125 14.6 Hematocrit 43.0 3.5 41.7 mg/dL Glucose, serum 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 mg/dL 26.0 3.0 25.0 Calcium, serum 9.55 0.525 10.1 Total cholesterol Triglycerides mg/dL mg/dL 24.75 149.5 253.0 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 0.72 4.3 Ratio 1.8 mcIU/mL TSH, high sensitivity, serum 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 four. Test results attributed to Abby Tudor are actual results obtaincd from an anonymous patient.