Chi-Square Distributions and Goodness of Fit

The degrees of freedom of the Chi Square distribution are equal to the number of standard normal deviates being summed (which is 12 in this case).

The mean of a Chi Square distribution is its degrees of freedom.

As the degrees of freedom of a Chi Square distribution increase, the Chi Square distribution begins to look more and more like a normal distribution. Thus, out of these choices, a Chi Square distribution with 10 df would look the most similar to a normal distribution.

Because three scores are sampled, the answer can be found using the Chi Square distribution with three degrees of freedom. A Chi Square calculator can be used to find that the probability of a Chi Square (with 3 $df$) being 9 or higher is .0293.