A population consists of the following N = 5 numbers: 2, 5, 6, 9, 27. Suppose a randomsample of size n = 3 is selected without replacement from this population.(a) [5 marks] Determine the sampling distribution of the sample range. Note that therange of a set of values is defined to be the difference between the largest value andthe smallest value

Apologies for the confusion, but it seems like there's a mix-up in the instructions. I'll proceed with answering the original question about the sampling distribution of the sample range.

Step 1: Identify all possible samples of size 3 from the population.

The population is {2, 5, 6, 9, 27}. The possible samples of size 3 without replacement are:

{2, 5, 6}, {2, 5, 9}, {2, 5, 27}, {2, 6, 9}, {2, 6, 27}, {2, 9, 27}, {5, 6, 9}, {5, 6, 27}, {5, 9, 27}, {6, 9, 27}

Step 2: Calculate the range for each sample.

The range is the difference between the largest and smallest value in each sample:

4, 7, 25, 7, 25, 25, 4, 22, 22, 21

Step 3: Create the sampling distribution of the sample range.

The sampling distribution of the sample range is:

Range: 4, 7, 21, 22, 25 Frequency: 2, 2, 1, 2, 3

This means, for example, that if we were to take many, many samples of 3 from the population, about 20% of those samples would have a range of 4, 20% would have a range of 7, 10% would have a range of 21, 20% would have a range of 22, and 30% would have a range of 25.