| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Probability calculation plus find unknown boundary |
| Difficulty | Moderate -0.8 This is a straightforward application of normal distribution with inverse standardization in part (a) requiring lookup of z-value for 20% upper tail, then solving for variance. Part (b) is direct probability calculation. Both parts are routine S1 exercises with no conceptual challenges beyond standard normal distribution manipulation. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(X > 23.8) = 0.2\) | M1 | |
| \(P(Z < \frac{23.3-22.8}{\sigma}) = 0.8\) | M1 | |
| \(\frac{0.5}{\sigma} = 0.8416\) | B1 | |
| \(\sigma = 0.5941; \sigma^2 = 0.3530\) | M1 A1 | |
| \(P(Z < \frac{21.82-22.8}{0.5941}) = P(Z < -1.65) = 0.0495\) | M2 A1 | (8) |
| $P(X > 23.8) = 0.2$ | M1 | |
| $P(Z < \frac{23.3-22.8}{\sigma}) = 0.8$ | M1 | |
| $\frac{0.5}{\sigma} = 0.8416$ | B1 | |
| $\sigma = 0.5941; \sigma^2 = 0.3530$ | M1 A1 | |
| $P(Z < \frac{21.82-22.8}{0.5941}) = P(Z < -1.65) = 0.0495$ | M2 A1 | (8) |An athlete believes that her times for running 200 metres in races are normally distributed with a mean of 22.8 seconds.
\begin{enumerate}[label=(\alph*)]
\item Given that her time is over 23.3 seconds in 20\% of her races, calculate the variance of her times. [5]
\item The record over this distance for women at her club is 21.82 seconds. According to her model, what is the chance that she will beat this record in her next race? [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q1 [8]}}