Understanding Normal Distribution in Health Metrics

Oct 19, 2024

Lecture Notes: Normal Distribution (Section 8E)

Introduction

  • Focus on normal distribution, particularly in relation to health metrics like cholesterol and blood pressure.
  • Importance of understanding cholesterol as one ages.

Cholesterol

  • Role: Key in heart and blood vessel health.
  • Monitoring: Most adults should check cholesterol every five years.
  • Statistical Analysis:
    • Use large data sets for mean and standard deviation.
    • Use distribution to find healthy cholesterol levels.
    • Z-scores can determine where an individual's cholesterol level falls in the distribution.

Using the Normal Distribution

  • Random variables are central to understanding distributions.
  • Use z-scores to determine distance from the mean.
  • Technology assists in calculating probabilities and percentiles.
  • Empirical Rule:
    • 68% within 1 SD, 95% within 2 SDs, 99.7% within 3 SDs.

Case Study: Cholesterol Levels

  • Mean: 191 mg/dl, Standard Deviation: 40.7 mg/dl.
  • Calculate probabilities for various cholesterol levels using normal distribution tools.
    • Example: Probability of cholesterol within 1 SD (150.3 to 231.7) is about 68.24%.
    • Cholesterol level < 200 mg/dl probability: 58.75%.
    • Borderline (200 to 239 mg/dl): 29.34%.
    • High cholesterol (> 240 mg/dl): Approximately 11.43%.
  • Z-scores: Useful for determining how far an individual is from the mean.

Blood Pressure

  • Definition: Systolic over diastolic readings.
  • Influenced by activity and daily variations.
  • Standard Ranges:
    • <120: Healthy
    • 120-140: Borderline

    • 140: High

Blood Pressure Case Studies

  • Different patients with varying means and standard deviations.
    • Example: Patient with mean 120, SD 11.9; probability of reading >140 is 4.64%.
    • For mean 130, SD 12.9, probability >140 is 21.91%.

Diagnosis Considerations

  • Repeated measurements needed to confirm diagnosis.
  • Z-scores or technology can help assess unusual readings.

Children's Blood Pressure

  • Varies with age and size.
  • Hypertension: Defined as above the 95th percentile.
    • Example: For an 8-year-old, mean 97, SD 9.4, the 95th percentile is 112.46.
  • Low Blood Pressure: Below the 5th percentile is critical.
    • Example: Value for 5th percentile in same group is 81.54.

Conclusion

  • Emphasis on using normal distribution and z-scores to analyze health data.
  • Importance of individual health checks and understanding statistical context.