The Normal Distribution · Hard problem

The distribution cannot be close to normal: the empirical rule would put about $16\%$ of scores above $10.5$, which is impossible.

About $68\%$ of scores lie between $7.5$ and $10.5$, by the empirical rule.

About $2.5\%$ of students scored below $6$, by the empirical rule.

The empirical rule applies to any data set with at least $30$ values.