To determine the percentage of patients with an age of onset ranging from 57 to 67 years, we need to apply the properties of a normal distribution. In a normal distribution, the mean represents the central point, and the standard deviation defines the spread of the data. Here, the mean age of onset is 62 years, and the standard deviation is 5 years. The range of 57 to 67 years corresponds to one standard deviation below the mean (62 - 5 = 57) to one standard deviation above the mean (62 + 5 = 67).
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean (i.e., between μ - σ and μ + σ, where μ is the mean and σ is the standard deviation). This is a well-established statistical principle, often referred to as the 68-95-99.7 rule (or empirical rule) in statistics. Specifically, 34% of the data lies between the mean and one standard deviation above the mean, and another 34% lies between the mean and one standard deviation below the mean, totaling 68% for the range spanning one standard deviation on both sides of the mean.
Let’s verify this:
The lower bound (57 years) is exactly one standard deviation below the mean (62 - 5 = 57).
The upper bound (67 years) is exactly one standard deviation above the mean (62 + 5 = 67).
Thus, the range from 57 to 67 years encompasses the middle 68% of the distribution.
Option A (34%) represents the percentage of patients within one standard deviation on only one side of the mean (e.g., 62 to 67 or 57 to 62), not the full range. Option C (95%) corresponds to approximately two standard deviations from the mean (62 ± 10 years, or 52 to 72 years), which is wider than the given range. Option D (99%) aligns with approximately three standard deviations (62 ± 15 years, or 47 to 77 years), which is even broader. Since the question specifies a range of one standard deviation on either side of the mean, the correct answer is 68%, corresponding to Option B.
In infection control, understanding the distribution of disease onset ages can help infection preventionists identify at-risk populations and allocate resources effectively, aligning with the CBIC’s focus on surveillance and data analysis (CBIC Practice Analysis, 2022). While the CBIC does not directly address statistical calculations in its core documents, the application of normal distribution principles is a standard epidemiological tool endorsed in public health guidelines, which inform CBIC practices.
References:
CBIC Practice Analysis, 2022.
Public Health Epidemiology Guidelines, Normal Distribution and Empirical Rule (commonly accepted statistical standards).
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