2. A standard test for diabetes is based on the glucose level X in blood after fasting a

prescribed time period. The mean fasting glucose level for a healthy person is u=5.31

mmol/L and the standard deviation is o= 0.58mmol/L. Assume that the levels of

glucose for healthy people are normally distributed.

a. What is the probability that a healthy person will have glucose level more than 5.7

mmol/L?

b. Decide if it is possible for a random sample of 50 healthy people to have average

glucose level more than 5.7 mmol/L?

c. 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.