Answer:

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Step-by-step explanation:

To construct the sampling distribution of the sample mean, we need to find all possible combinations of three cards that can be drawn from the population of six cards. There are a total of 20 possible combinations of three cards that can be drawn from a population of six cards, and we can list them as follows:

1 2 3

1 2 4

1 2 5

1 2 6

1 3 4

1 3 5

1 3 6

1 4 5

1 4 6

1 5 6

2 3 4

2 3 5

2 3 6

2 4 5

2 4 6

2 5 6

3 4 5

3 4 6

3 5 6

4 5 6

Next, we need to calculate the mean of each of these samples. For example, the mean of the first sample (1 2 3) is (1+2+3)/3 = 2. Similarly, we can calculate the mean of each of the other samples.

Once we have calculated the mean of each sample, we can plot them on a frequency distribution. The x-axis will represent the sample means, and the y-axis will represent the frequency of occurrence of each sample mean.

The resulting sampling distribution of the sample mean will be approximately normal if the population from which the samples are drawn is normally distributed or if the sample size is sufficiently large (n > 30) and the population has a finite variance. However, since the population in this case consists of only six cards, it is not normally distributed, and the sample size is small (n=3), so the sampling distribution will not be exactly normal. Nonetheless, we can still construct the sampling distribution as described above.