| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Rounded or discrete from continuous |
| Difficulty | Standard +0.3 This is a straightforward S1 normal distribution question requiring standard z-score calculations and basic understanding of independence. Part (a) involves routine standardization and table lookup. Part (b) tests understanding that continuous distributions have P(X=k)=0, independence means multiplying probabilities, and that sample means follow N(μ, σ²/n). All techniques are standard bookwork 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 transformation5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
3 Each day, Margot completes the crossword in her local morning newspaper. Her completion times, $X$ minutes, can be modelled by a normal random variable with a mean of 65 and a standard deviation of 20 .
\begin{enumerate}[label=(\alph*)]
\item Determine:
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( X < 90 )$;
\item $\mathrm { P } ( X > 60 )$.
\end{enumerate}\item Given that Margot's completion times are independent from day to day, determine the probability that, during a particular period of 6 days:
\begin{enumerate}[label=(\roman*)]
\item she completes one of the six crosswords in exactly 60 minutes;
\item she completes each crossword in less than 60 minutes;
\item her mean completion time is less than 60 minutes.\\
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-07_2484_1709_223_153}
\end{center}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S1 2010 Q3 [13]}}