Draw all possible samples of size n=3 with replacement from thepopulation 2, 5, and 9. Compute the sampling distribution of sampleproportion of even numbers and verify that

To draw all possible samples of size n=3 with replacement from the population 2, 5, and 9, we need to consider all the possible combinations of these numbers.

The population consists of 2, 5, and 9. Since we are sampling with replacement, each number can be selected more than once in a single sample.

To compute the sampling distribution of the sample proportion of even numbers, we need to determine the proportion of even numbers in each sample.

Let's list all the possible samples of size 3 with replacement from the population:

Sample 1: (2, 2, 2) Sample 2: (2, 2, 5) Sample 3: (2, 2, 9) Sample 4: (2, 5, 2) Sample 5: (2, 5, 5) Sample 6: (2, 5, 9) Sample 7: (2, 9, 2) Sample 8: (2, 9, 5) Sample 9: (2, 9, 9) Sample 10: (5, 2, 2) Sample 11: (5, 2, 5) Sample 12: (5, 2, 9) Sample 13: (5, 5, 2) Sample 14: (5, 5, 5) Sample 15: (5, 5, 9) Sample 16: (5, 9, 2) Sample 17: (5, 9, 5) Sample 18: (5, 9, 9) Sample 19: (9, 2, 2) Sample 20: (9, 2, 5) Sample 21: (9, 2, 9) Sample 22: (9, 5, 2) Sample 23: (9, 5, 5) Sample 24: (9, 5, 9) Sample 25: (9, 9, 2) Sample 26: (9, 9, 5) Sample 27: (9, 9, 9)

Now, let's compute the sample proportion of even numbers for each sample.

Sample 1: (2, 2, 2) - All numbers are even, so the sample proportion of even numbers is 1. Sample 2: (2, 2, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 3: (2, 2, 9) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 4: (2, 5, 2) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 5: (2, 5, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 6: (2, 5, 9) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 7: (2, 9, 2) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 8: (2, 9, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 9: (2, 9, 9) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 10: (5, 2, 2) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 11: (5, 2, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 12: (5, 2, 9) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 13: (5, 5, 2) - Three numbers are even, so the sample proportion of even numbers is 1. Sample 14: (5, 5, 5) - Three numbers are even, so the sample proportion of even numbers is 1. Sample 15: (5, 5, 9) - Three numbers are even, so the sample proportion of even numbers is 1. Sample 16: (5, 9, 2) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 17: (5, 9, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 18: (5, 9, 9) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 19: (9, 2, 2) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 20: (9, 2, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 21: (9, 2, 9) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 22: (9, 5, 2) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 23: (9, 5, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 24: (9, 5, 9) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 25: (9, 9, 2) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 26: (9, 9, 5) - Two numbers are even, so the sample proportion of even numbers is 2/3. Sample 27: (9, 9, 9) - Three numbers are even, so the sample proportion of even numbers is 1.

By examining the sample proportions of even numbers for each sample, we can verify the sampling distribution. The sampling distribution should show the distribution of these sample proportions.