| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Discrete Probability Distributions |
| Type | Construct probability distribution from scenario |
| Difficulty | Standard +0.3 This is a straightforward probability distribution question requiring basic probability calculations, expectation, variance, and scaling for multiple trials. Part (i) involves listing outcomes and their probabilities (routine). Part (ii) requires finding E(X), Var(X), then scaling by 120 - all standard Further Statistics techniques with no novel insight needed. Slightly above average difficulty due to the two-part structure and variance calculation, but well within typical Further Maths exercises. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
A game is played as follows. A fair six-sided dice is thrown once. If the score obtained is even, the amount of money, in £, that the contestant wins is half the score on the dice, otherwise it is twice the score on the dice.
\begin{enumerate}[label=(\roman*)]
\item Find the probability distribution of the amount of money won by the contestant. [3]
\item The contestant pays £5 for every time the dice is thrown. Find the standard deviation of the loss made by the contestant in 120 throws of the dice. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2017 Q3 [8]}}