Question

1. the distribution is symmetric because if the distribution were cut in half, both sides would be the same shape.

Explanation:

To determine if the distribution is symmetric, we check the mirror - image property. For a distribution represented on a number line (like the dot plot here), a symmetric distribution has the same shape on either side of the center. If we imagine cutting the distribution (the set of dots) in half, we can see that the pattern of dots on the left - hand side of the center and the right - hand side of the center is the same. For example, the number of dots at position 0 and position 4, position 1 and position 3, and around position 2 (the center) have a corresponding pattern that makes the two halves mirror images of each other. So the reasoning that if the distribution were cut in half, both sides would be the same shape is a correct way to identify symmetry.

Answer:

The reasoning is correct. The distribution is symmetric as the two halves (when cut) have the same shape.