According to a recent study the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Assume that blood pressure is normally distributed.
According to a recent study the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Assume that blood pressure is normally distributed.
(a) What is the random variable?
(b) Find the probability that a person in China has blood pressure of 140 mmHg or more.
(c) Find the probability that a person in China has blood pressure of 135 mmHg or less.
(d) Is it unusual for a person in China to have a blood pressure of 135 mmHg or less? Why or why not?
(e) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
(f) What is the 90th percentile blood pressure for the people in China? (That is, what is the blood pressure which 90 percent of the people have less than?
Continuing with this problem, suppose now a sample of 15 people are chosen from the above normal distribution and we are interested in the mean blood pressure of such a sample.
(g) Describe the distribution of the sample means: What is its shape? What is its mean? What is its standard deviation?
(h) Find the probability that the sample mean blood pressure of 15 people in China is 140 mmHg or more.
(i) Would it be unusual to find a sample mean blood pressure of 15 people in China of 140 mmHg or more? Why or why not?
