Question:

Blood pressure measurements are obtained from a sample of individuals with no known medical conditions. For systolic blood pressure (SBP), the mean measurements and associated standard deviations (SDs) are shown by age group for men and women:

	Men	Women
Age group	Mean SBP (mm Hg) ± SD	Mean SBP (mm Hg) ± SD
35-44	120 ± 20	124 ± 18
45-54	131 ± 21	137 ± 24
55-64	141 ± 19	140 ± 20

If hypertension is defined as SBP >140 mm Hg, approximately what percentage of men age 35-44 in this sample will be classified as having hypertension, assuming a normal (Gaussian) distribution?

16%

34%

50%

68%

84%

95%

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Explanation:

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A normal (Gaussian) distribution refers to a symmetrical, bell-shaped distribution with a fixed proportion of observations lying within a certain distance of the mean. This distance is called the standard deviation (SD) and reflects the degree of dispersion from the mean. According to the properties of this distribution, 68% of observations lie within 1 SD on either side of the mean, with half (ie, 68/2 = 34%) above and half (34%) below the mean. The remaining 32% (= 100% − 68%) lie outside 1 SD from the mean, with half (ie, 32/2 = 16%) above and the other half (16%) below 1 SD from the mean. In addition, 95% of all observations lie within 2 SDs of the mean, and 99.7% of all observations lie within 3 SDs of the mean. This is the 68-95-99.7 rule.

For men age 35-44 in this sample, the mean systolic blood pressure (SBP) is 120 mm Hg with an SD of 20 mm Hg. Therefore, subjects with SBP >140 mm Hg (to fit the proposed definition of hypertension) represent observations >1 SD above the mean. Based on the 68-95-99.7 rule, 32% of observations (= 100% − 68%) lie outside 1 SD from the mean, with half (16%) above and half (16%) below 1 SD from the mean. Therefore, 16% of men age 35-44 have SBP >140 mm Hg.

(Choices B, C, D, and E) Based on the 68-95-99.7 rule, 34% of subjects lie either 1 SD above the mean or 1 SD below the mean. In men age 35-44:

34% have SBP 100-120 mm Hg, 34% have SBP 120-140 mm Hg, and, 68% have SBP 100-140 mm Hg.
Half (50%) have SBP above the mean (ie, >120 mm Hg) and half have SBP below the mean (<120 mm Hg).
Given that 84% = 50% + 34%, this could represent the sum of those with SBP 100-120 mm Hg (34%) and those with SBP >120 mm Hg (50%): in other words, those with SBP >100 mm Hg.

(Choice F) Based on the 68-95-99.7% rule, 95% of observations lie within 2 SDs (eg, 2 × 20 = 40 mm Hg) of the mean (eg, 120 mm Hg) (ie, SBP between 80 mm Hg [= 120 − 40] and 160 mm Hg [= 120 + 40]).

Educational objective:
In a normal (bell-shaped) distribution, 68% of all values are within 1 standard deviation (SD) of the mean; 95% are within 2 SD of the mean; and 99.7% are within 3 SD of the mean.