| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Mixed calculations with boundaries |
| Difficulty | Standard +0.3 This is a straightforward S1 normal distribution question requiring standard z-score calculations and one binomial probability application. Part (a) is routine standardization, part (b) is a simple percentile calculation, and part (c) combines normal probability with basic binomial—all standard textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04c Calculate binomial probabilities2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks |
|---|---|
| \(P(Z < \frac{25 - 21.5}{2.2}) = P(Z < 1.59) = 0.9441\) | M2 A1 |
| Answer | Marks |
|---|---|
| \(P(Z > \frac{19 - 21.5}{2.2}) = P(Z > -1.14) = 0.8729 \therefore 87.3\%\) | M2 A1 |
| Answer | Marks |
|---|---|
| \(P(Z < \frac{20 - 21.5}{2.2}) = P(Z < -0.68) = 0.2483\) | M1 A1 |
| \(P(\text{2 of 3} < 20) = 3 \times 0.2483^2 \times 0.7517 = 0.139\) | M2 A1 |
| (11) |
**Part (a)**
$P(Z < \frac{25 - 21.5}{2.2}) = P(Z < 1.59) = 0.9441$ | M2 A1 |
**Part (b)**
$P(Z > \frac{19 - 21.5}{2.2}) = P(Z > -1.14) = 0.8729 \therefore 87.3\%$ | M2 A1 |
**Part (c)**
$P(Z < \frac{20 - 21.5}{2.2}) = P(Z < -0.68) = 0.2483$ | M1 A1 |
$P(\text{2 of 3} < 20) = 3 \times 0.2483^2 \times 0.7517 = 0.139$ | M2 A1 |
| (11) |3. The time it takes girls aged 15 to complete an obstacle course is found to be normally distributed with a mean of 21.5 minutes and a standard deviation of 2.2 minutes.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that a randomly chosen 15 year-old girl completes the course in less than 25 minutes.
A 13 year-old girl completes the course in exactly 19 minutes.
\item What percentage of 15 year-old girls would she beat over the course?
Anyone completing the course in less than 20 minutes is presented with a certificate of achievement. Three friends all complete the course one afternoon.
\item What is the probability that exactly two of them get certificates?
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [11]}}