1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with= 140+X mg/dl and= X+1 mg/dl, where X is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:

1. Once?
2. X+2 times, where X is the last digit of your student ID?
3. X+4 times, where X is the last digit of your student ID?

Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.

2. Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 9X percent reliable, this means that the test will yield an accurate positive result in 99% of the cases where the disease is actually present. Gestational diabetes affects X+1 percent of the population in our patient's age group, and that our test has a false positive rate of X+4 percent. Use your knowledge of Bayes' Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2:

1. If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes?
2. What is the probability of having the disease given that you test positive?
3. If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes?
4. What is the probability of having the disease given that you tested negative?