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 13.4 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) 123.9 mm Hg, 148.1 mm Hg
B) 118.8 mm Hg, 153.2 mm Hg
C) 114 mm Hg, 158 mm Hg
D) 115 mm Hg, 159 mm Hg
Is the answer B?
Can some one give me some hints please..
The answer isn't even in your options; the correct answer is 119.9mm Hg, 160.1mm Hg.
The correct answer is C.
You have to include the CI=90% which is a zscore = 1.645
Take the SD of 13.4 and multiply it by the zscore. Then subtract and add 136. Round up and the answer is C.
To find the two blood pressures that meet the given criteria, we need to determine the range that includes 90% of all blood pressures. We know that the mean is midway between these two blood pressures.
First, let's find the z-scores corresponding to the two endpoints of this range. Since we want to capture 90% of the data, we need to find the z-scores that correspond to the cutoff points of 5% on either side of the mean.
Using a standard normal distribution table or a calculator, we can find the z-score for a cumulative probability of 0.05. The z-score for a cumulative probability of 0.05 is approximately -1.645.
Next, we can find the actual blood pressure values corresponding to these z-scores using the formula:
X = μ + (z * σ)
where X is the blood pressure, μ is the mean, z is the z-score, and σ is the standard deviation.
First Blood Pressure:
X1 = 136 + (-1.645 * 13.4)
X1 ≈ 112.95
Second Blood Pressure:
X2 = 136 + (1.645 * 13.4)
X2 ≈ 159.05
Now we have the range of blood pressures that includes 90% of the data: (112.95 mm Hg, 159.05 mm Hg).
Comparing the given choices:
A) 123.9 mm Hg, 148.1 mm Hg: Not within the range
B) 118.8 mm Hg, 153.2 mm Hg: Not within the range
C) 114 mm Hg, 158 mm Hg: Within the range
D) 115 mm Hg, 159 mm Hg: Within the range
Therefore, the correct answer is C) 114 mm Hg, 158 mm Hg.