Final answer:
The proportion of patients in a given population considered healthy based on their CD4 counts can be calculated using the Z-score and the standard normal distribution table, taking into account the mean and standard deviation of the CD4 count distribution.
Step-by-step explanation:
The student has asked about the proportion of patients in a population with a normal CD4 count distribution (µ=237, σ=43) who can be considered healthy. Given that a CD4 count over 350 cells/μL is typically required for HIV patients to maintain a relatively normal life with minimal complications beyond medication side-effects, we need to calculate the proportion of patients whose CD4 counts are above this threshold.
To do this, the Z-score formula (Z = (X - µ)/σ) can be used to find the Z-value corresponding to a CD4 count of 350. With µ=237 and σ=43, the Z-value for a CD4 count of 350 is calculated as Z= (350 - 237)/43, which simplifies to approximately 2.63. Using the standard normal distribution table, we can determine the proportion of patients with a Z-value less than 2.63, and then subtract this from 1 to find the proportion with a Z-value above 2.63, or in other words, with a CD4 count above 350.
The proportion found represents the percentage of patients in the considered population who could be considered healthy in terms of their CD4 counts. This percentage is crucial for understanding the effectiveness of antiretroviral therapies and the overall health status of the population in terms of HIV progression.