| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Probability calculation plus find unknown boundary |
| Difficulty | Standard +0.3 This is a straightforward application of normal distribution with inverse standardization in part (a) and direct probability calculation in part (b). Students need to use z-tables and basic algebraic manipulation, but the question follows a standard template with no conceptual challenges beyond routine S1 techniques. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(P\left(Z > \frac{100-\mu}{12.6}\right) = 0.0764\) giving \(\frac{100-\mu}{12.6} = 1.43\) and \(\mu = 82.0\) | M1 A1 M1 A1 | |
| (b) \(P(75 < R < 80) = P(-0.55 < Z < -0.16)\) | M1 A1 | |
| \(= 0.436 - 0.291 = 0.145\) | M1 A1 A1 | Total: 9 marks |
(a) $P\left(Z > \frac{100-\mu}{12.6}\right) = 0.0764$ giving $\frac{100-\mu}{12.6} = 1.43$ and $\mu = 82.0$ | M1 A1 M1 A1 |
(b) $P(75 < R < 80) = P(-0.55 < Z < -0.16)$ | M1 A1 |
$= 0.436 - 0.291 = 0.145$ | M1 A1 A1 | Total: 9 marksThe rainfall at a weather station was recorded every day of the twentieth century. One year is selected at random from the records and the total rainfall, in cm, in January of that year is denoted by $R$. Assuming that $R$ can be modelled by a normal distribution with standard deviation $12.6$, and given that P$(R > 100) = 0.0764$,
\begin{enumerate}[label=(\alph*)]
\item find the mean of $R$, [4 marks]
\item calculate P$(75 < R < 80)$. [5 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [9]}}