7.25 Blood pressure Vincenzo Baranello was diagnosed with high blood pressure. He was able to keep his blood pressure in control for several months by taking blood pressure medicine (amlodipine besylate). Baranello’s blood pressure is monitored by taking three readings a day, in early morning, at midday, and in the evening.

a. During this period, the probability distribution of his systolic blood pressure reading had a mean of 130 and a standard deviation of 6. If the successive observations behave like a random sample from this distribution, find the mean and standard deviation of the sampling distribution of the sample mean for the three observations each day.

b. Suppose that the probability distribution of his blood pressure reading is normal. What is the shape of the sampling distribution? Why?

c. Refer to part

b. Find the probability that the sample mean exceeds 140, which is considered problematically high. (Hint: Use the sampling distribution, not the probability distribution for each observation.)