| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2002 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Find p then binomial probability |
| Difficulty | Standard +0.3 Part (i) requires recognizing that P(X > 3.6) = 0.5 implies μ = 3.6, then using z-tables to find σ from the second probability—straightforward application of normal distribution properties. Part (ii) is a standard binomial probability calculation (at least 2 from 4). Both parts are routine S1 techniques with no novel insight required, making this 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 |
\begin{enumerate}[label=(\roman*)]
\item In a normal distribution with mean $\mu$ and standard deviation $\sigma$, $\text{P}(X > 3.6) = 0.5$ and $\text{P}(X > 2.8) = 0.6554$. Write down the value of $\mu$, and calculate the value of $\sigma$. [4]
\item If four observations are taken at random from this distribution, find the probability that at least two observations are greater than 2.8. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2002 Q6 [8]}}