3. The blood cholesterol levels of men age 55 to 64 are approximately Normal, with mean 224 milligrams per deciliter (mg/dl) and standard deviation 39 mg/dl. A physician will randomly select 76 men age 55 to 64 and will compute the sample mean. For each question sketch a graph of the distribution demonstrating the value you are asked to find.

a. What interval contains the sample mean for 99.7% of all samples of size 76?

b. What is the probability that the sample mean is greater than 233 mg/dl?