| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Probability distribution from formula |
| Difficulty | Moderate -0.8 This is a straightforward S1 probability distribution question requiring routine calculations: completing a table using a given formula, summing probabilities to find k, calculating expectation using the standard formula, and reading off a probability from the table. All steps are mechanical with no problem-solving or insight required. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(r\) | 0 | 1 | 2 | 3 | 4 |
| P(\(X = r\)) | \(6k\) | \(10k\) |
The number, $X$, of children per family in a certain city is modelled by the probability distribution P($X = r$) = $k(6 - r)(1 + r)$ for $r = 0, 1, 2, 3, 4$.
\begin{enumerate}[label=(\roman*)]
\item Copy and complete the following table and hence show that the value of $k$ is $\frac{1}{50}$. [3]
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$r$ & 0 & 1 & 2 & 3 & 4 \\
\hline
P($X = r$) & $6k$ & $10k$ & & & \\
\hline
\end{tabular}
\item Calculate E($X$). [2]
\item Hence write down the probability that a randomly selected family in this city has more than the mean number of children. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q5 [6]}}