Chapter 5, Problem 10P

A study was conducted assessing the effect of observer training on measurement of blood pressure based on NHANES data from 1999–2000 (Ostchega, et al., [1]). A goal was that the difference in recorded blood pressure between the observer and trainer be ≤ 2 mm Hg in absolute value. It was reported that the mean difference in systolic blood pressure (SBP) between observers and trainers (i.e., mean observer SBP minus trainer SBP) = mean (Δ) was 0.189 mm Hg with sd = 2.428 mm Hg.

If we assume that the distribution of Δ is normally distributed, then what % of (observer, trainer) pairs have a mean difference of ≥ 2 mm Hg in absolute value (i.e., either ≥ 2 mm Hg or ≤ −2 mm Hg)?