Two Independent Random Samples Are Drawn from Two Normal Populations

Short Answer

Two independent random samples are drawn from two normal populations. The sample sizes are 20 and 25, respectively. The parameters of these populations are: $$\begin{array} { | l | l | } \hline \text { Population 1: } & \mu = 505 , \sigma = 10 \\\hline \text { Population } 2 : & \mu = 475 , \sigma = 7 \\\hline\end{array}$$ Find the probability that the difference between the two sample means $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is between 25 and 35.