| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Topic | Confidence intervals |
| Type | Calculate CI for proportion |
| Difficulty | Standard +0.8 This is a capture-recapture problem requiring understanding of the underlying probability model, construction of a confidence interval for a proportion (requiring normal approximation and appropriate z-value), and then the non-trivial step of transforming this interval via the reciprocal relationship N = 400/p. The transformation of confidence intervals through non-linear functions is conceptually demanding and goes beyond routine A-level statistics. |
| Spec | 5.05d Confidence intervals: using normal distribution |
A random sample of 400 seabirds is taken from a colony, ringed, and returned, unharmed, to the colony. After a suitable period of time has elapsed, a second random sample of 400 seabirds is taken, and 20 of this second sample are found to be ringed. You may assume that the probability that a seabird is captured is independent of whether or not it has been ringed and that the colony remains unchanged at the time of the second sampling.
\begin{enumerate}[label=(\roman*)]
\item Estimate the number of seabirds in the colony. [1]
\item Find a 98% confidence interval for the proportion of seabirds in the colony which are ringed. [5]
\item Deduce a 98% confidence interval for the number of seabirds in the colony. [2]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2014 Q3 [8]}}