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According to a health information website, the distribution of adults' diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard deviation 20. A diastolic pressure above 100 for an adult is classified as very high blood pressure. About what percentage of adults have very high blood pressure according to this criterion?

User Firien
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Final answer:

Approximately 6.68% of adults are estimated to have diastolic blood pressure above 100 mm Hg, classified as very high, based on the Normal distribution with mean 70 and standard deviation 20.

Step-by-step explanation:

The question is asking us to find the percentage of adults who have a diastolic blood pressure above 100 mm Hg, given the distribution is Normal with mean 70 and standard deviation 20. To find this, we use the standard normal distribution (z-scores). A z-score represents how many standard deviations an element is from the mean.

First, we calculate the z-score for a diastolic pressure of 100:

z = (X - μ) / σ

Where X is the value of interest (100 mm Hg), μ is the mean (70 mm Hg), and σ is the standard deviation (20 mm Hg).

z = (100 - 70) / 20 = 1.5

Now we look up this z-score on a standard normal distribution table or use a calculator that provides the cumulative area to the left of our z-score. We are interested in the area to the right of z = 1.5 since we want the percentage of adults with blood pressure higher than 100 mm Hg.

The table or calculator might tell us that the area to the left of z = 1.5 is approximately 0.9332 (which is 93.32%). Therefore, the area to the right is 1 - 0.9332 = 0.0668 or 6.68%.

Thus, approximately 6.68% of adults are estimated to have very high diastolic blood pressure according to this criterion.

User Samuel Taylor
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