Answer to Question #120415 in Statistics and Probability for Mark

Question

Blood pressure is an important health indicator in humans. Blood pressure results from two forces. One, the systolic pressure, is created by the heart as it pumps blood into the arteries and through the circulatory system. The other, the diastolic pressure, is the force of the arteries as they resist the blood flow. In a particular population the systolic pressures are normally distributed with a mean of 110 mmHg and a standard deviation of 8 mmHg.

(a) Systolic pressure less than 120 mmHg are considered normal. What percentage of the population has normal systolic blood pressures?

(b) Systolic pressures above 140 mmHg are considered hypertensive and in need of medical intervention. What proportion of the population will have these values?

(c) Systolic pressures of 120 to 139 mmHg are considered

Answer 1

a) P(x<120)

z=(x-μ)/σ=(120-110)/8=1.25, using table P(x<120)=0.894=89.4%

b) P(x>140)=1-P(x<140)

z=(x-μ)/σ=(140-110)/8=3.75, using table P(x<140)=0.99991

P(x>140)=1-0.99991=9.0e-5=0.009%

c) P(120<x<139)=P(x<139)-P(x<120)=

P(x<120)=0.894

P(x<139)

z=(139-110)/8=3.63, using table P(x<139)=0.99986

P(120<x<139)=0.99986-0.894=0.1059=10.59%