Question 1194763
**A. List all samples of size 4 and find the mean of each sample:**

1. **List all possible combinations of 4 cities:**

   * F, D, Y, T 
   * F, D, Y, R
   * F, D, T, R
   * F, Y, T, R
   * D, Y, T, R 

2. **Calculate the mean of each sample:**

   * F, D, Y, T: (42 + 39 + 36 + 33) / 4 = 37.5
   * F, D, Y, R: (42 + 39 + 36 + 30) / 4 = 36.75
   * F, D, T, R: (42 + 39 + 33 + 30) / 4 = 36
   * F, Y, T, R: (42 + 36 + 33 + 30) / 4 = 35.25
   * D, Y, T, R: (39 + 36 + 33 + 30) / 4 = 34.5

**B. Construct the sampling distribution of the sample mean**

The sampling distribution of the sample mean is a table or a graph that shows the probability of each possible sample mean occurring.

| Sample Mean | Frequency |
|---|---|
| 37.5 | 1 |
| 36.75 | 1 |
| 36 | 1 |
| 35.25 | 1 |
| 34.5 | 1 |

**Note:** 

* Since we are sampling without replacement from a small population, the probabilities associated with each sample mean are not all equal. 
* To calculate the exact probabilities, we would need to consider the combinations and permutations of selecting the cities.

This exercise demonstrates the concept of sampling distribution. By taking multiple samples and calculating their means, we can observe how the sample means vary around the population mean. In larger populations, the sampling distribution of the mean tends to approach a normal distribution, which is a key concept in statistical inference.