Two independent random samples are drawn from two normal populations. The sample sizes are 20 and 25, respectively. The parameters of these populations are: $$\begin{array} { | l | l | } \hline \text { Population 1: } & \mu = 505 , \sigma = 10 . \ \hline \text { Population 2: } & \mu = 4750 , \sigma = 7 . \ \hline \end{array}$$ Find the probability that the difference between the two sample means (X₁-bar - X₂-bar) is between 25 and 35.

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The Answer of Two independent random samples are drawn from two normal populations. The sample sizes are 20 and 25, respectively. The parameters of these populations are: $$\begin{array} { | l | l | } \hline \text { Population 1: } & \mu = 505 , \sigma = 10 . \ \hline \text { Population 2: } & \mu = 4750 , \sigma = 7 . \ \hline \end{array}$$ Find the probability that the difference between the two sample means (X₁-bar - X₂-bar) is between 25 and 35.

Two Independent Random Samples Are Drawn from Two Normal Populations