Solution — 2022 Question 6 Normal Distribution

Let $X$ be the volume of milk in a randomly chosen carton.

$X \sim N (4.82, σ^{2})$

\begin{matrix} P (X < 4.64) & = 0.05 \\ P (Z < \frac{4.64 - 4.82}{σ}) & = 0.05 \\ \frac{4.64 - 4.82}{σ} & = - 1.6449 \\ 4.64 - 4.82 & = - 1.6449 σ \\ σ & = 0.109 43 \\ = 0.109 ∎ (to 3 s.f.) \end{matrix}

apply standardization and inverse norm to find mu/sigma