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 μ = 72 and σ = 10. Use the Distributions tool to help answer the questions that follow. The minimum z-score necessary to be in the top 20% of the diastolic blood pressure distribution is z =0.842 . Use this z-score to determine X, the corresponding diastolic blood pressure score. X = 80.42 This score, X, is the 80th percentile of diastolic blood pressure scores among teenagers. The percentile rank of this score is 80% . Diastolic blood pressure between 80 and 89 is considered prehypertension. What percentage of teenagers have diastolic blood pressure in this range? 19.23% 23.22% 16.73% 21.56% What percentage of teenagers have hypotension—that is, diastolic blood pressure below 60? 11.51% 9.57% 13.51% 23.22%

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 4GP

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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 μ = 72 and σ = 10.

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

The minimum z-score necessary to be in the top 20% of the diastolic blood pressure distribution is z =0.842 .

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

X = 80.42

This score, X, is the 80th percentile of diastolic blood pressure scores among teenagers. The percentile rank of this score is 80% .

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

19.23%

23.22%

16.73%

21.56%

What percentage of teenagers have hypotension—that is, diastolic blood pressure below 60?

11.51%