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Two Independent Random Samples Are Drawn from Two Normal Populations

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Two independent random samples are drawn from two normal populations. The sample sizes are 20 and 25, respectively. The parameters of these populations are:  Population 1: μ=505,σ=10 Population 2:μ=475,σ=7\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 Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } is between 25 and 35.

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