| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | First success on specific trial |
| Difficulty | Standard +0.3 This is a straightforward application of the geometric distribution with clearly defined success probability (0.3). Parts (a) and (b) require direct formula substitution, while part (c) involves calculating mean and standard deviation then finding probabilities within that range—all standard textbook exercises requiring recall and basic computation rather than problem-solving insight. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | 0.72×0.3 |
| = 0.147 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.1 | For geometric |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (b) | P(At least 5) = 0.24(01) |
| [1] | 1.1 | 0.74 or 1−0.3(1+0.7+0.72+0.73) oe |
| 1 | (c) | 10 |
| Answer | Marks |
|---|---|
| (1−0.76) = 0.88(2351) | B1 |
| Answer | Marks |
|---|---|
| [5] | 3.1b |
| Answer | Marks |
|---|---|
| 1.1 | 1 |
Question 1:
1 | (a) | 0.72×0.3
= 0.147 | M1
A1
[2] | 3.3
1.1 | For geometric
Accept 0.15
1 | (b) | P(At least 5) = 0.24(01) | B1
[1] | 1.1 | 0.74 or 1−0.3(1+0.7+0.72+0.73) oe
1 | (c) | 10
Mean = soi
3
1−0.3
Variance =
0.32
√70
Standard deviation =
3
10 √70
Evaluate 𝑡ℎ𝑒𝑖𝑟 ( ± )
3 3
and identify their correct integer range
(1−0.76) = 0.88(2351) | B1
M1
A1
M1
A1 FT
[5] | 3.1b
1.1a
1.1
3.4
1.1 | 1
Accept 3.3
0.3
(2.78886…)
P(0.54 < 𝑋 < 6.12)
= P(𝑋 ≤ 6)
FT their 𝐸(𝑋) and 𝑆𝐷(𝑋) provided more than one positive
integer included in their range.1 A fair spinner has ten sectors, labelled $1,2 , \ldots , 10$. In order to start a game, Kofi has to obtain an 8,9 or 10 on the spinner.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that Kofi starts the game on the third spin.
\item Find the probability that Kofi takes at least 5 spins to start the game.
\item Determine the probability that the number of spins required to start the game is within 1 standard deviation of its mean.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2023 Q1 [8]}}