In a recent study, the Centers for Disease Control reported that diastolic blood pressures (in mmHg) of adult women in the U.S. are approximately normally distributed with mean 80.5 and standard deviation 9.9.
a. What proportion of women have blood pressures lower than 70?
b. What is the 80th percentile of blood pressures?
c. A woman has a blood pressure of 84. What percentile is her blood pressure on?
d. A diastolic blood pressure greater than 90 is classified as hypertension (high blood pressure). What proportion of women have hypertension?
(a) z = (70-80.5)/9.9=-1.06. The area to the right of z= ?1.06 is 0.1446.
(b) The z-score of the 80th percentile is ? 0.84.
The 80th percentile is therefore ? 80.5 + 0.84(9.9) = 88.8.
(c) z = (84-80.5)/9.9=0.35. The area to the left of z= 0.35 is 0.6368.
Therefore a score of 84 is on the 64th percentile, approximately.
(d) z = (90-80.5)/9.9=0.96 . The area to the left of z= 0.96 is 0.8315.
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