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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=4750,σ=7.\begin{array} { | l | l | } \hline \text { Population 1: } & \mu = 505 , \sigma = 10 . \\\hline \text { Population 2: } & \mu = 4750 , \sigma = 7 . \\\hline\end{array} Find the probability that the difference between the two sample means (X1-bar - X2-bar) is between 25 and 35.


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