Question

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.

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.

Answer 1

d) P(Sample mean of 400 or more)

= P(z > 13.28)

= 0.0000

e) Yes, the calculation will be valid even for a skewed population because as per central limit theorem, the sampling distribution of sample mean follows a normal population if the sample size is large (n > 30), regardless of the shape of the population.