| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Multiple probability calculations only |
| Difficulty | Easy -1.3 This is a straightforward normal distribution question requiring only basic recall and standard procedures: reading off the standard deviation from notation, and performing routine z-score calculations using tables. All three parts are textbook exercises with no problem-solving or conceptual challenge, making it easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks |
|---|---|
| (a) \(1.7\) | B1; M1 A1 |
| (b) \(P(X < 0) = P(Z < -2/1.7) = P(Z < -1.176) = 0.12\) | B1; M1 A1 |
| (c) \(P(0.6 < X < 3.4) = P(-0.8235 < Z < 0.8235) = 2(0.294) = 0.588\) | M1 A1 M1 A1 |
**(a)** $1.7$ | B1; M1 A1 |
**(b)** $P(X < 0) = P(Z < -2/1.7) = P(Z < -1.176) = 0.12$ | B1; M1 A1 |
**(c)** $P(0.6 < X < 3.4) = P(-0.8235 < Z < 0.8235) = 2(0.294) = 0.588$ | M1 A1 M1 A1 |
**Total marks: 7**
---The random variable $X$ has the normal distribution $N(2, 1.7^2)$.
\begin{enumerate}[label=(\alph*)]
\item State the standard deviation of $X$. [1 mark]
\item Find $P(X < 0)$. [2 marks]
\item Find $P(0.6 < X < 3.4)$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [7]}}