A cross-sectional study is conducted to evaluate the intraocular pressure (IOP) in a population of healthy adults over the age of . The collected IOP measurements are determined to follow a normal distribution with a mean of mm Hg. The researchers note that approximately participants ( of the cohort) have an IOP greater than mm Hg.
Based on these findings, what is the variance of the intraocular pressure in this population?
Cevap: 9 mm Hg^2
Cevap
9
The correct answer is . In a normal distribution, the empirical rule dictates that approximately of values fall within one standard deviation (SD) of the mean. Because the distribution is symmetrical, the remaining of values fall outside this range, with located in the upper tail (above SD) and in the lower tail (below SD). The study states that of participants have an IOP greater than mm Hg, meaning mm Hg represents exactly SD from the mean of mm Hg. The standard deviation is therefore mm Hg. Variance is mathematically defined as the square of the standard deviation (). Therefore, the variance is .
Adım Adım Çözüm
Anahtar Kavram
Application of the empirical (68-95-99.7) rule to identify the standard deviation from population percentiles, and calculating variance as the square of the standard deviation.