Can you say "Bayes Theorem"? Look it up and tell us what you find.
Blood sugar healthy people distributed with average 84 and standard deviation of 10, blood sugar sick people distributed with an average 150 and standard deviation of 20. The researchers tested and found that the probability of a healthy person has a sugar level higher than 110 is 0.025, the probability of a sick person has a sugar level higher than 110 is 0.964. What is the probability that tested person with sugar level higher than 110 sick?
Also the information about means and standard deviations is redundant, the quoted survey results are sufficient. The means and standard deviations are useless with out an assumption about the distribution of blood sugar level.