9.87 A factory operates with two machines of type A and one machine of type B. The weekly repair costs Y for type A machines are normally distributed with mean and variance . The weekly repair costs X for machines of type B are also normally distributed, but with mean and variance . The expected repair cost per week for the factory is then

. Suppose Y1,…,Yn denotes a random sample on costs for type A machines and X1,…,Xn denotes an independent random sample on costs for type B machines. Use these data to construct a 95% confidence interval for .