The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 13.8 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 90% of all blood pressures are between them.

Question

Quizplus · Accepted Answer

Given that 90% of the values lie between these two blood pressures and the distribution is normal, we use the concept of standard deviations in a normal distribution. For 90% of the data to be within these values, we are looking at the blood pressures that lie within ±1.645 standard deviations from the mean (since the z-score for 90% confidence interval is approximately ±1.645). Calculating the values: Mean ± 1.645(Standard Deviation) = 136 ± 1.645(13.8) = 136 ± 22.7 = 113.3 mm Hg, 158.7 mm Hg.

The Systolic Blood Pressures of the Patients at a Hospital