February/March 2026 Paper 62

Anita has a dice with sides numbered 1, 2, 3, 4, 5, 6. The score on one throw is denoted by $X$. Assuming that the dice is fair, show that $\mathrm{Var}(X)=\frac{35}{12}$.

Anita suspects that the dice is not fair. She thinks that low scores are more likely than high scores. She intends to throw the dice 50 times, and if the mean score is less than 3, she will conclude that the dice is not fair. It is now given that the dice is not fair and $\mathrm{E}(X)=2.5$. Assuming that $\mathrm{Var}(X)=\frac{35}{12}$, calculate the probability of a Type II error. You may assume that a continuity correction is not needed.

State what is meant by a Type II error in this context.

The sample mean score from Anita's 50 throws of the dice was 2.9. Explain why it is not possible for Anita to make a Type II error.