| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Probability calculation plus find unknown boundary |
| Difficulty | Standard +0.3 This is a straightforward application of normal distribution with standard procedures: standardizing to find probabilities from tables, then using independence for part (b)(i) and sampling distribution of the mean for part (b)(ii). All techniques are routine S1 content with no conceptual challenges or 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) |
2 The diameter, $D$ millimetres, of an American pool ball may be modelled by a normal random variable with mean 57.15 and standard deviation 0.04 .
\begin{enumerate}[label=(\alph*)]
\item Determine:
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( D < 57.2 )$;
\item $\mathrm { P } ( 57.1 < D < 57.2 )$.
\end{enumerate}\item A box contains 16 of these pool balls. Given that the balls may be regarded as a random sample, determine the probability that:
\begin{enumerate}[label=(\roman*)]
\item all 16 balls have diameters less than 57.2 mm ;
\item the mean diameter of the 16 balls is greater than 57.16 mm .
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S1 2011 Q2 [11]}}