Among diabetics, the fasting blood glucose level X may be assumed to be approximately normally distributed with mean 106 mg/100 ml and standard deviation 8 mg/100 ml.

(a) Sketch a graph of the density for X. Indicate on this graph the probability that a randomly selected diabetic will have a blood glucose level between 90 and 122 mg/100 ml. Find this probability.

(b) Find P[X 5 120 mg/100 ml].

(c) Find the point that has the property that 25% of all diabetics have a fasting glucose level of this value or lower.

(d) If a randomly selected diabetic is found to have fasting blood glucose level in excess of 130, do you think there is cause for concern? Explain, based on the probability of this occurring naturally.