Solution — 2022 Question 6 Normal Distribution
Let be the volume of milk in a randomly chosen carton.
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$̲ X \sim \mathrm{N} \left( 4.82, \sigma^2 \right)
\begin{align*} \mathrm{P}\left(X < 4.64\right) &= 0.05 \\ \mathrm{P}\left(Z < \frac{4.64 - 4.82}{\sigma}\right) &= 0.05 \\ \frac{4.64 - 4.82}{\sigma} &= -1.6449 \\ 4.64 - 4.82 &= -1.6449\sigma \\ \sigma &= 0.109\,43 \\ &= 0.109\; \QED \text{ (to 3 s.f.)} \end{align*}$$ ParseError: {align*} can be used only in display mode.
[apply standardization and inverse norm to find mu/sigma]