A National Health Service used extensive surveys of medical professionals to establish that, in 2005-2010, the mean serum cholesterol level of males aged 20-74 was 211. The standard deviation was 90.

a) An individual male in this age group is measured and has a value of 400 (high?). Compute his z-score and find the probability that any individual male has at least this cholesterol level in this population.

b) Describe the expected sampling distribution of the mean cholesterol if samples of size 40 were taken from this population - state the shape, mean and standard deviation of this sampling distribution.

c) Sketch both the population and the sampling distribution on the same axis, ensuring correct labelling

d) Random men were approached leaving a fast food shop and, if in the age group, were asked to participate in a cholesterol study. The serum cholesterol levels were measured for 40 such men and a mean of 400 was obtained. If these men were representative of our population in general what is the probability that a sample mean (from n=40) will have this value of 400 or more?

e) Would these calculations above in d) be valid if the population distribution was skewed? EXPLAIN clearly, stating the concept or theory that is involved in this situation.