3 Research suggests that the mean reading age of a child about to start secondary school is 10.75 . The reading ages, \(X\) years, of a random sample of 80 children who were about to start secondary school in a particular district were measured, and the results are summarised as follows. $$\mathrm { n } = 80 \quad \sum \mathrm { x } = 893 \quad \sum \mathrm { x } ^ { 2 } = 10267$$

1. Test at the \(5 \%\) significance level whether the mean reading age of children about to start secondary school in this district is not 10.75 .
2. A student wrote: "Although we do not know that the distribution of \(X\) is normal, the central limit theorem allows us to assume that it is, as the sample size is large." This statement is incorrect. Give a corrected version of the student's statement.