High Blood Pressure A patient visits her doctor with concern

High Blood Pressure

A patient visits her doctor with concerns about her blood pressure. If the systolic blood pressure exceeds 150, the patient is considered to have high blood pressure and medication may be prescribed. The problem is that there is considerable variation in a patient’s systolic blood pressure readings during a given day.

1.If a patient’s systolic blood pressure readings during a given day has a normal distribution with a mean of 160 mm mercury and a standard deviation of 20mm, what is the probability that a single measurement will fail to detect that the patient has high blood pressure?

2. If five measurements are taken at various times of the day, what is the probability that all five will fail to detect that the patient has high blood pressure?

3. If five measurements are taken at various times of the day what is the probability that their average will be less than 150 and hence fail to detect that the patient has high blood pressure?

4. If the mean of several measurements is to be used as an indicator of the patient’s actual blood pressure, how many measurements would be required so that the probability is at most 1% of failing to detect that the patient has high blood pressure?

Solution

Blood pressure measurement during the day is normal with mean = 160 and sigma = 20

a) Prob in a single test fail to detect BP

= P(X<150)

= P(Z<-10/20) = 0.5-0.1915

= 0.3085

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2) Here no of reading X is binomial with p for a single success = 0.3085

Hence P(X=0 in 5 trials) = 0.3085⁵ = 0.0028

3) Here sample size = 5

Std error of sample = 20/rt 5 = 8.944

P(X bar<150 in a sample of 5)

= P(Z<-10/8.944) = P(z<-1.2) = 0.1151

4) Margin of error < 1% = 0.01

If n is the sample size, then 20/rtn < 0.01

rtn > 2000

n > 4,000,000