Final answer:
1. The population mean µ of the given population is 3. 2. The population standard deviation σ is approximately 1.095. 3. Sampling with replacement from the population involves randomly selecting objects from the population and recording them.
Step-by-step explanation:
1. To find the population mean, µ, you need to sum up all the values in the population and divide that sum by the number of objects in the population. In this case, the sum of the population is 1 + 2 + 3 + 4 + 5 = 15. Dividing 15 by 5, you get a mean of 3.
2. To find the population standard deviation, σ, you need to calculate the variance first. The variance is the average of the squared differences between each value in the population and the mean. The squared differences for this population are (1-3)^2, (2-3)^2, (3-3)^2, (4-3)^2, and (5-3)^2. Summing up these squared differences, you get 2 + 1 + 0 + 1 + 2 = 6. Dividing 6 by 5, you get a variance of 1.2. Taking the square root of the variance, you get the standard deviation, which is approximately 1.095.
3. To take samples of size n=2 from the population with replacement, you randomly select two objects from the population and record them. You repeat this process multiple times to obtain multiple samples. For example, one possible sample could be {1, 3}, where you randomly selected object 1 and object 3. Another possible sample could be {5, 2}. The key is to randomly select the objects each time and record them in the sample.