Medical researchers have devised a test that quantitatively measures a person’s risk of heart disease.  The test scores for the general public are approximately normally distributed with a mean of 50. On the test, higher test scores indicate a higher risk of heart disease.  An advocate of long-distance running believes that marathon runners should have a lower risk of heart disease than the general public.

 A random sample of 20 marathon runners is selected and each is tested for their risk of heart disease.  Their test scores have a mean of 43.7 and a standard deviation of 4.2. Construct a 90% confidence interval for µ, the true mean score for all marathon runners.