Independent Random Samples of 100 Observations Each Are Chosen from Two

Essay

Independent random samples of 100 observations each are chosen from two normal
populations with the following means and standard deviations. $$\begin{array} { l l } \text { Population 1 } & \text { Population 2 } \\\mu _ { 1 } = 15 & \mu _ { 2 } = 13 \\\sigma _ { 1 } = 3 & \sigma _ { 2 } = 2\end{array}$$
Find the mean and standard deviation of the sampling distribution of $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)$ .