The serum cholesterol levels in men aged 18 to 24 are normally distributed with mean of 178.1 and standard deviation of 40.7. All unites are in mg/100mg, and the data are based upon the National Health Survey. A group of 9 men aged 18 to 24 is randomly chosen.
(a) Determine the probability that the serum cholesterol level of a man in the group is between 200 and 250?
(b) Determine the probability that the average serum cholesterol level of the group is between 200 and 250.
(c) Determine the probability that are at least 2 men in the group whose serum cholesterol level is at most 230.
(d) Assume 90% of men's serum cholesterol level is less than c. What is the value of c?