A sample of 314 patients between the ages of 38 and 82 were given a combination of the drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.94 millimole per liter. Assume the population standard deviation is σ = 0.18.

a. Construct a 98% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs.

b. Should this confidence interval be used to estimate the mean reduction in total cholesterol for patients over the age of 85?

Explain.

c. Based on the confidence interval constructed in part (a), is it likely that the mean reduction in cholesterol level is less than 0.90?