. Independent random samples are taken from the output of two machines on a production line.The weight of each item is of interest. From the first machine, a sample of size 36 is taken, with sample mean weight of 120 grams and a sample variance of 4. From the second machine, a sample of size 64 is taken, with a sample mean weight of 130 grams and a sample variance of 5. It is assumed that the weights of items from the first machine are normally distributed with mean 1 and variance 2 and that the weights of items from the second machine are normally distributed with mean 2 and variance 2 (that is, the variances are assumed to be equal). Find a 99 percent confidence interval for 1 2, the difference in population means.