Can someone help me understand how to get started on this problem?
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 mean1 - mean2.
b. Can you conclude that the variable mean1-mean2 is normally distributed?
c. 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.