As is the case for other professions which require dexterity and athleticism, the career span of a professional dancer is relatively short. A random sample of 16 retired professional dancers is collected. The average length of their dancing careers was 14.7 years with a standard deviation of 5.6 years. Find a 90% confidence interval for the mean length of a dancing career. You may assume the variable is normally distributed. You must write an interpretation that is specific to this problem.