| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Basic E(X) and Var(X) calculation |
| Difficulty | Easy -1.3 This is a straightforward application of standard binomial distribution formulas with n=4, p=0.2. Part (a) requires direct substitution into P(X=k), part (b) uses the standard formulas E(X)=np and Var(X)=np(1-p), and part (c) applies linear transformations of expectation and variance. All steps are routine recall with no problem-solving or insight required. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02d Binomial: mean np and variance np(1-p) |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | Use of B(4, 0.2) soi |
| P(X = 3) = 0.0256 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.1 | 16 |
| 625 | 2.56% |
| (b) | E(X) = 0.8 oe |
| Var(X) = 0.64 oe | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | (i) | Expected total = 100 + 0.8 × 50 |
| = 60 p oe | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 1.1 | M1 for 0.5(their E(X)) 1 |
| Answer | Marks |
|---|---|
| With appropriate monetary unit | SCB1 if following M0 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | (ii) | Standard deviation = 50 0.64 40 poe |
| [1] | 1.1 | With appropriate monetary unit |
| Mark final answer | N.B. £0.40p is A0 |
Question 1:
1 | (a) | Use of B(4, 0.2) soi
P(X = 3) = 0.0256 | M1
A1
[2] | 3.3
1.1 | 16
625 | 2.56%
(b) | E(X) = 0.8 oe
Var(X) = 0.64 oe | B1
B1
[2] | 1.1
1.1
(c) | (i) | Expected total = 100 + 0.8 × 50
= 60 p oe | M1
A1
[2] | 3.1b
1.1 | M1 for 0.5(their E(X)) 1
or 50(their E(X)) 100
e.g. “loss of £0.60”
With appropriate monetary unit | SCB1 if following M0
60p seen
N.B. -£0.60p is A0
(c) | (ii) | Standard deviation = 50 0.64 40 poe | B1
[1] | 1.1 | With appropriate monetary unit
Mark final answer | N.B. £0.40p is A01 In a game at a charity fair, a spinner is spun 4 times.\\
On each spin the chance that the spinner lands on a score of 5 is 0.2 .\\
The random variable $X$ represents the number of spins on which the spinner lands on a score of 5 .
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { P } ( X = 3 )$.
\item Find each of the following.
\begin{itemize}
\item $\mathrm { E } ( X )$
\item $\operatorname { Var } ( X )$
\end{itemize}
One game costs $\pounds 1$ to play and, for each spin that lands on a score of 5 , the player receives 50 pence.
\item \begin{enumerate}[label=(\roman*)]
\item Find the expected total amount of money gained by a player in one game.
\item Find the standard deviation of the total amount of money gained by a player in one game.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2019 Q1 [7]}}