| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Mixed calculations with boundaries |
| Difficulty | Moderate -0.3 This is a standard normal distribution question requiring routine z-score calculations and inverse normal lookup. Part (a) involves straightforward standardization and table/calculator use, part (b) requires working backwards from a percentage using the inverse normal. While it has multiple parts, all techniques are core S1 material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
3 The weight, $X$ grams, of talcum powder in a tin may be modelled by a normal distribution with mean 253 and standard deviation $\sigma$.
\begin{enumerate}[label=(\alph*)]
\item Given that $\sigma = 5$, determine:
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( X < 250 )$;
\item $\mathrm { P } ( 245 < X < 250 )$;
\item $\mathrm { P } ( X = 245 )$.
\end{enumerate}\item Assuming that the value of the mean remains unchanged, determine the value of $\sigma$ necessary to ensure that $98 \%$ of tins contain more than 245 grams of talcum powder.\\
(4 marks)
\includegraphics[max width=\textwidth, alt={}, center]{adf1c0d2-b0a6-4a2f-baf2-cfb45d771315-07_38_118_440_159}\\
\includegraphics[max width=\textwidth, alt={}, center]{adf1c0d2-b0a6-4a2f-baf2-cfb45d771315-07_40_118_529_159}
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2009 Q3 [10]}}