What is true when a normal distribution of hemoglobin (Hb) values is assumed?

Properties of Normal Distribution

When hemoglobin values follow a normal distribution, approximately 99% of subjects fall within 3 standard deviations of the mean, and the standard deviation is the square root of variance—making statements A and E correct. 1

Key Statistical Properties of Normal Distribution

Standard Deviation Ranges

• Approximately 68% of values fall within 1 standard deviation of the mean (not 62% as stated in option C) 1
• Approximately 95% of values fall within 2 standard deviations of the mean (not 92% as stated in option B) 1
• Approximately 99.7% of values fall within 3 standard deviations of the mean, confirming option A is correct 1

Relationship Between Variance and Standard Deviation

• Standard deviation is mathematically defined as the square root of variance, making option E definitively correct 1
• This fundamental relationship holds regardless of the distribution type 1

Application to Hemoglobin Data

When analyzing hemoglobin values with a standard deviation of 2 g/dL under normal distribution assumptions:

• The range of mean ± 1 SD captures approximately 68% of patients (e.g., if mean is 14 g/dL, then 12-16 g/dL contains ~68% of values) 1
• The range of mean ± 2 SD captures approximately 95% of patients (e.g., 10-18 g/dL contains ~95% of values) 1
• The range of mean ± 3 SD captures approximately 99.7% of patients (e.g., 8-20 g/dL contains ~99.7% of values) 1

Clinical Context for Hemoglobin Reference Ranges

• Normal hemoglobin distributions are commonly used to establish reference ranges, with the 5th and 95th percentiles often defining normal limits 2
• For adult males, normal hemoglobin ranges from 13.5-17.5 g/dL, and for adult females 12.0-15.5 g/dL 3

Why Other Options Are Incorrect

Option B is incorrect: 92% does not correspond to any standard deviation multiple in a normal distribution; 2 standard deviations captures 95%, not 92% 1

Option C is incorrect: 62% does not correspond to 1 standard deviation; the correct value is approximately 68% 1

Option D regarding M Scores: This option is vague and not a standard statistical concept related to normal distributions 1

Common Pitfalls

• Confusing the empirical rule percentages: The 68-95-99.7 rule is fundamental and should be memorized 1
• Assuming normality without verification: Visual inspection via Q-Q plots or statistical tests (Shapiro-Wilk for n<50, Kolmogorov-Smirnov for n≥50) should confirm normality before applying these rules 4
• Ignoring heavy-tailed distributions: Real biological data may deviate from perfect normality, particularly with mixed populations or varying measurement precision 5