Question: A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population. Moreover, the variable is normally distributed on each of the two populations.

1. For independent samples of sizes 9 and 4, respectively, determine the mean and standard deviation of \(\bar{x}_{1}-\bar{x}_{2}\)
2. Can you conclude that the variable \(\bar{x}_{1}-\bar{x}_{2}\) is normally distributed? Explain your answer.
3. Determine the percentage of all pairs of independent samples of sizes 9 and 4 , respectively, from the two populations that have the property that the difference between the sample means is between \(-10\) and 10 .

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