[6 marks]

A standard test for diabetes is based on the glucose levelin blood after fasting a prescribed time period. The mean fasting glucose level for a healthy person is mmol/L and the standard deviation is mmol/L. Assume that the levels of glucose for healthy people are normally distributed.

What is the probability that a healthy person will have glucose level more than 5.7 mmol/L?

Decide if it is possible for a random sample of 50 healthy people to have average glucose level more than 5.7 mmol/L?

Recall here that when samples of size n are randomly drawn from a normal population with mean and standard deviation , the sample averagehas a normal distribution with mean and standard deviation .

If we drop now the assumption of normality of glucose levels and answer the question in b. above using the same method, will our answer be significantly different from the answer that we got in b.? You must justify your answer.

[Hint: Use CLT].