| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Standard two probabilities given |
| Difficulty | Moderate -0.3 This is a standard S1 normal distribution problem requiring students to find μ and σ from two given probabilities, then use these to find another probability. While it involves multiple steps (finding z-scores, solving simultaneous equations, standardizing), these are routine techniques practiced extensively in S1 with no novel problem-solving required. Slightly easier than average due to its predictable structure. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
6. The time taken, in minutes, by children to complete a mathematical puzzle is assumed to be normally distributed with mean $\mu$ and standard deviation $\sigma$. The puzzle can be completed in less than 24 minutes by $80 \%$ of the children. For $5 \%$ of the children it takes more than 28 minutes to complete the puzzle.
\begin{enumerate}[label=(\alph*)]
\item Show this information on the Normal curve below.
\item Write down the percentage of children who take between 24 minutes and 28 minutes to complete the puzzle.
\item \begin{enumerate}[label=(\roman*)]
\item Find two equations in $\mu$ and $\sigma$.
\item Hence find, to 3 significant figures, the value of $\mu$ and the value of $\sigma$.
A child is selected at random.
\end{enumerate}\item Find the probability that the child takes less than 12 minutes to complete the puzzle.\\
\includegraphics[max width=\textwidth, alt={}, center]{ca8418eb-4d35-40f4-af40-77503327ae52-11_314_1255_1375_356}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2014 Q6 [13]}}