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.
a. For independent samples of sizes 9 and 4, 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 9 and 4, respectively, from the two populations with the property that the difference x1 − x2 between the sample means is between −10 and 10.