A nurse is investigating the birth weights of​ non-premature babies. She selects a random sample of 41 such​ babies, and found a mean weight of 3506.4 grams and a sample standard deviation of 494.2 grams. Find a 95​% confidence interval for the mean birth weight of all ​non-premature babies. Show your calculation for the confidence interval as well as the final confidence interval rounded to one decimal place. Then write a sentence that gives the interpretation of your confidence​ interval, including the correct units.