Solve the problem.
-The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 138 mm Hg and a standard deviation of 13.5 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.
A) 120.7 mm Hg, 155.3 mm Hg
B) 115.8 mm Hg, 160.2 mm Hg
C) 125.9 mm Hg, 150.2 mm Hg
D) 116.8 mm Hg, 161.2 mm Hg

Question

Quizplus · Accepted Answer

We need to find the blood pressures that are midway between them and contain 90% of all blood pressures.

Using the empirical rule, we know that 90% of the data falls within 1.645 standard deviations from the mean.

To find the two blood pressures, we can use the formula:

Lower bound = mean - (z-score)(standard deviation)
Upper bound = mean + (z-score)(standard deviation)

Let x be the blood pressure we are looking for. We know that:

mean = (x1 + x2)/2, where x1 and x2 are the two blood pressures
x1 = 2(mean) - x2

Substituting the values we know:

mean = 138
standard deviation = 13.5
z-score = 1.645

Solving for x2:

138 + 1.645(13.5) = x2

x2 = 160.2 mm Hg

Using x1 = 2(mean) - x2:

x1 = 115.8 mm Hg

Therefore, the two blood pressures that are midway between them and contain 90% of all blood pressures are 115.8 mm Hg and 160.2 mm Hg, which correspond to choice B.

Solve the Problem. -The Systolic Blood Pressures of the Patients at a Hospital