A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population. Moreover, the variable is normally distributed on each of the two populations. a. For independent samples of sizes 3 and 6, respectively, determine the mean and standard deviation of x1 - x2.b. Can you conclude that the variable x1 - x2 is normally distributed? Explain your answer.c. Determine the percentage of all pairs of independent samples of sizes 4 and 16, respectively, from the two populations with the property that the difference x1 - x2 between the sample means is between -3 and 4.

Question

A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population. Moreover, the variable is normally distributed on each of the two populations.

a. For independent samples of sizes 3 and 6, respectively, determine the mean and standard deviation of x1 - x2.
b. Can you conclude that the variable x1 - x2 is normally distributed? Explain your answer.
c. Determine the percentage of all pairs of independent samples of sizes 4 and 16, respectively, from the two populations with the property that the difference x1 - x2 between the sample means is between -3 and 4.

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