In a chemical process, three bottles of a standard fluid are emptied into a larger container. A study of the individual bottles shows that the mean value of the contents is 13 ounces and the standard deviation is 0.07 ounces. If three bottles form an i. i.d. sample,
(a) Find the expected value and the standard deviation of the volume of liquid emptied into the larger container.
(b) If the content of the individual bottles is normally distributed, what is the probability that the volume of liquid emptied into the larger container will be in excess of 39.1 ounces?