A patient visits her doctor with concerns about

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?

5. The breaking strengths (say, y) for one-foot- square samples of a particular synthetic fabric are approximately normally distributed with a mean of 2,280 pounds per square inch (psi) and a standard deviation of 10.6 psi.

A. Find the probability of selecting a 1-foot -square sample of material at random that on testing would have a breaking strength in excess of 2,240 psi.

B. Describe the sampling distribution for based on random samples of 25 one-foot sections. (you need to name the distribution and give the mean and standard deviation of the distribution)