Question

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 a considerable variation in a patient’s systolic blood pressure readings during a given day.

A. If a patient’s systolic readings during a given day have a normal distribution with a mean of 155 and a standard deviation of 20, what is the probability that a single measurement will fail to detect that the patient has high blood pressure?

B. If six measurements are taken at various times during the day, what is the probability that the average blood pressure reading will be less than 150 and hence fail to indicate that the patient has a high blood pressure problem?

C. How many measurements would be required so that the probability is at most 5% of failing to detect that the patient has high blood pressure?

Answer 1

Given:

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.

Mean, = 155

Standard deviation, = 20

Let X : represent a sigle measurement on blood pressure of a patient .

X follows the Normal distribution.

X ~ Normal ( = 155, ^2 = 20^2)

a) The probability that a single measurement will fail to detect that the patient has high blood pressure :

Therefore

a)  The probability that a single measurement will fail to detect that the patient has high blood pressure is 0.4013

b) The probability that the average blood pressure reading will be less than 150 and hence fail to indicate that the patient has a high blood pressure problem is 0.2709

c) The measurements would be required so that the probability is at most 5% of failing to detect that the patient has high blood pressure is n = 11