| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2024 |
| Session | October |
| Paper | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Mixed calculations with boundaries |
| Difficulty | Moderate -0.8 This is a straightforward S1 normal distribution question requiring standard z-score calculations and inverse normal lookup. Part (a) involves standardizing and using tables to find P(X ≥ 190), while part (b) requires finding the value corresponding to the 10th percentile. Both are routine textbook exercises with no problem-solving insight needed, making this easier than average for A-level. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(X \sim N(170, 16^2)\) | ||
| \(P(X > 190) = P\left(Z > \frac{190 - 170}{16}\right) \left[= P(Z > 1.25)\right]\) | M1 | For standardising using 190, 170 and 16 (May be implied by 1.25) |
| \(\left[= 1 - 0.8944\right] = 0.1056\) | A1 | awrt 0.106 Do not ISW |
| (b) \(P(X > d) = 0.9\) | ||
| \(\frac{d - 170}{16} = -1.2816\) or \(\frac{170 - d}{16} = 1.2816\) (Calc value ±1.28155…) | M1 A1 | For standardising and setting = z value, where \(1 < |
| \(d = 149.494...\) | dA1 | awrt 149 Dependent on previous A1 149.5 or awrt 149 |
**(a)** $X \sim N(170, 16^2)$ | |
$P(X > 190) = P\left(Z > \frac{190 - 170}{16}\right) \left[= P(Z > 1.25)\right]$ | M1 | For standardising using 190, 170 and 16 (May be implied by 1.25)
$\left[= 1 - 0.8944\right] = 0.1056$ | A1 | awrt 0.106 Do not ISW
**(b)** $P(X > d) = 0.9$ | |
$\frac{d - 170}{16} = -1.2816$ or $\frac{170 - d}{16} = 1.2816$ (Calc value ±1.28155…) | M1 A1 | For standardising and setting = z value, where $1 < |z| < 2$
$d = 149.494...$ | dA1 | awrt 149 Dependent on previous A1 149.5 or awrt 149
**Total: 5 marks**\begin{enumerate}
\item In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
\end{enumerate}
The distances, $m$ miles, a motorbike travels on a full tank of petrol can be modelled by a normal distribution with mean 170 miles and standard deviation 16 miles.\\
(a) Find the probability that, on a randomly selected journey, the motorbike could travel at least 190 miles on a full tank of petrol.
The probability that, on a randomly selected journey, the motorbike could travel at least $d$ miles on a full tank of petrol is 0.9\\
(b) Find the value of $d$
\hfill \mbox{\textit{Edexcel S1 2024 Q4}}