A patient visits her doctor with concerns about her blood pressure. If the systolic bloodâ€ƒ 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 patientâ€™s systolic blood pressure readings during a given day.
a. If a patientâ€™s systolic readings during a given day have a normal distribution with aÂ mean of 160 mm mercury and a standard deviation of 20 mm, what is the probability that a single measurement will fail to detect that the patient has high blood pressure?
b. If five 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 toÂ indicate that the patient has a high blood pressure problem?
c. How many measurements would be required so that the probability of failing to detect that the patient has high blood pressure is at most 1%.