For the general population, the mean glucose level is normally distributed with mean 100 mg/dL and standard deviation 20 mg/dL. A blood sugar level less than 140 mg/dL is normal. A reading of more than 200 mg/dL indicates diabetes (i.e., the patient is diagnosed with diabetes).

(a) (10 pts) If we randomly selected a person from the general population, what is the probability that his/her blood sugar level is smaller than 98 mg/dL?

(b) (10 pts) If we lower the diabetes threshold from 200 mg/dL to 140 mg/dL. What is the proportion of people who are considered to have diabetes under the new threshold but they were not considered to have diabetes under the old threshold (i.e., 200 mg/dL)?

(c) (10 pts) Let us set the diabetes threshold as 200 mg/dL. Assume that there is a patient who has blood sugar normally distributed with mean 205 mg/dL and standard deviation 30 mg/dL (i.e., this patient is diabetic). If one measurement is made for this person, what is the probability that this person will be misdiagnosed?

If possible can you explain the answer well?

Thank you!