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Problem 3 [18 points]. Among diabetics, the fasting blood glucose level G may be as- sumed to be approximately normally distributed with mean 106 milligrams per 100 milli itres (mg/100 m) and standard deviation of 8 milligrams per 100 millilitres. Use and show probability notation for the problems below: a) (2 points) Without computing, under this distribution, do you think it will be very likely that a diabetic will have a fasting blood glucose level over 122 mg/100ml? Briefly explain
b) (3 points) What is the 80th percentile of fasting blood glucose levels of diabetics? Interpret this value.
c) (3 points) What is the range of (the most common) fasting blood glucose levels of 80% of diabetics?
d) (3 points) A diabetic is selected at random. Find the probability that their fasting blood glucose level is between 100 and 120 ml/100ml.
e) (5 points) Using your result from Problem 2, part (b)(i), state the probability distribution of the average fasting blood glucose level of 3 randomly selected diabetics. What is the probability that their average fasting blood glucose level will exceed 110 mg/100 ml?
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