| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Mixed calculations with boundaries |
| Difficulty | Standard +0.3 This is a straightforward normal distribution question requiring standard z-score calculations and sampling distribution application. All parts use routine techniques (finding probabilities, inverse normal, and sampling distribution of means) with no conceptual challenges beyond textbook exercises, making it slightly easier than average for A-level. |
| 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) |
5 When a particular make of tennis ball is dropped from a vertical distance of 250 cm on to concrete, the height, $X$ centimetres, to which it first bounces may be assumed to be normally distributed with a mean of 140 and a standard deviation of 2.5.
\begin{enumerate}[label=(\alph*)]
\item Determine:
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( X < 145 )$;
\item $\mathrm { P } ( 138 < X < 142 )$.
\end{enumerate}\item Determine, to one decimal place, the maximum height exceeded by $85 \%$ of first bounces.
\item Determine the probability that, for a random sample of 4 first bounces, the mean height is greater than 139 cm .
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q5 [15]}}