| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Calculate simple probabilities |
| Difficulty | Standard +0.3 This is a straightforward S2 uniform distribution question requiring standard formulas for mean/variance, a simple probability calculation involving an absolute value inequality, and a binomial probability application. All techniques are routine for this module with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf |
| Answer | Marks |
|---|---|
| Mean \(= 16\) | A1 |
| Variance \(= \frac{1}{12}(28 - 4)^2 = 48\) | M1 A1 |
| \(= P(13 < X < 19)\) | M1 |
| \(= 6 \times \frac{1}{24} = \frac{1}{4}\) | M1 A1 |
| Let \(Y =\) no. within 3 cm of middle \(\therefore Y \sim B(12, \frac{1}{4})\) | M1 |
| \(P(Y > 4) = 1 - P(Y \leq 4) = 1 - 0.8424 = 0.1576\) | M1 A1 |
Mean $= 16$ | A1 |
Variance $= \frac{1}{12}(28 - 4)^2 = 48$ | M1 A1 |
$= P(13 < X < 19)$ | M1 |
$= 6 \times \frac{1}{24} = \frac{1}{4}$ | M1 A1 |
Let $Y =$ no. within 3 cm of middle $\therefore Y \sim B(12, \frac{1}{4})$ | M1 |
$P(Y > 4) = 1 - P(Y \leq 4) = 1 - 0.8424 = 0.1576$ | M1 A1 |
---3. In an old computer game a white square representing a ball appears at random at the top of the playing area, which is 24 cm wide, and moves down the screen. The continuous random variable $X$ represents the distance, in centimetres, of the dot from the left-hand edge of the screen when it appears. The distribution of $X$ is rectangular over the interval [4,28].
\begin{enumerate}[label=(\alph*)]
\item Find the mean and variance of $X$.
\item Find $\mathrm { P } ( | X - 16 | < 3 )$.
During a single game, a player receives 12 "balls".
\item Find the probability that the ball appears within 3 cm of the middle of the top edge of the playing area more than four times in a single game.\\
(3 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q3 [9]}}