One 40 year old faculty member was diagnosed with high blood pressure. He was able to keep his blood pressure in control for several months by taking a certain blood pressure medication. He monitored his blood pressure by taking three readings a day- early morning, mid-day, and in the evening.
a) During the months when he was monitoring his blood pressure, 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 shape of the probability distribution of his blood pressure is normal. What is the shape of the sampling distribution?
c)Based on your answer to b, find the probability that the sample mean exceeds 140, which is considered problematically high.