1. In a Framingham study, serum cholesterol were measured for a large number of healthy males. The population was followed for 16 years. At the end of the time, the men were divided into 2 groups: those who had developed coronary disease and those who had not. The distributions of the initial serum cholesterol levels for each group were found to be approximately normal. Among individuals who eventually developed coronary disease, the mean serum cholesterol level was d= 244 mg/100 ml and the standard deviation was d=51 mg/100ml; for those who did not go on to develop the disease, the mean serum cholesterol was nd= 219 mg/100 ml and the standard deviation was d=41 mg/100ml.
2. Suppose that an initial serum cholesterol level of 260 mg/100ml was used to predict coronary heart disease. What is the probability of correctly predicting heart disease for a man who will go on to develop it?
3. Using the cutpoint in (a), What is the probability of predicting heart disease for a man who will not go on to develop it?

4. Using the cutpoint in (a), What is the probability of failing to predict heart disease for a man who will develop it?

5. What would happen to the probabilities of false positives and false negative errors if the cutoff point for predicting heart disease was lowered to 250 mg/100 ml?

6. In ths population, does initial serum cholesterol appear to be useful for predicting coronary heart disease? Why or why not?