Teenagers who do not sleep well or long enough may have a higher risk of raised blood pressure, which could lead to cardiovascular disease later in life. The odds of raised blood pressure increase 3.5 times for those who have trouble falling asleep at night or who wake up too early and 2.5 times for those with sleeping periods of fewer than 6.5 hours.

A health psychologist is interested in studying teenagers who have diastolic blood pressure scores in the top 20%. Diastolic blood pressure scores for teenagers follow a normal distribution with = 72 and = 10.

Use the Distributions tool to help answer the questions that follow.

Note: To find the probability above or below a z-score, click on the normal curve icon with one line, and position the line at the appropriate z-score on the horizontal axis. The areas under the standard normal curve above and below the z-score will be displayed to the left and right of the vertical line, respectively. To find the probability between two z-scores, click on the normal curve icon with two lines, and position the left line at the lower z-score and the right line at the higher z-score. The area under the normal curve between the vertical lines will be displayed in blue.

Standard Normal Distribution

Mean =0.0

Standard Deviation =1.0

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-1

0

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z

The minimum z-score necessary to be in the top 20% of the diastolic blood pressure distribution is z = .

Use this z-score to determine X, the corresponding diastolic blood pressure score.

X =

This score, X, is the percentile of diastolic blood pressure scores among teenagers. The percentile rank of this score is .

Diastolic blood pressure between 80 and 89 is considered prehypertension. What percentage of teenagers have diastolic blood pressure in this range?

21.56%

19.23%

16.73%

23.22%

What percentage of teenagers have hypotensionthat is, diastolic blood pressure below 60?

23.22%

9.57%

13.51%

11.51%