| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2023 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Standard two probabilities given |
| Difficulty | Standard +0.3 Part (a) is a straightforward standardization requiring recognition that μ-σ is one standard deviation below the mean (z=-1). Part (b) involves setting up two equations using inverse normal tables and solving simultaneously—a standard A-level technique but requiring careful algebra. Part (c) uses symmetry properties of normal distributions. Overall, this is a routine normal distribution question slightly above average difficulty due to the algebraic manipulation in part (b), but all techniques are standard bookwork. |
| Spec | 2.05b Hypothesis test for binomial proportion |
The random variable $Y$ has the distribution $\text{N}(\mu, \sigma^2)$.
\begin{enumerate}[label=(\alph*)]
\item Find $\text{P}(Y > \mu - \sigma)$. [1]
\item Given that $\text{P}(Y > 45) = 0.2$ and $\text{P}(Y < 25) = 0.3$, determine the values of $\mu$ and $\sigma$. [6]
\end{enumerate}
The random variables $U$ and $V$ have the distributions $\text{N}(10, 4)$ and $\text{N}(12, 9)$ respectively.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item It is given that $\text{P}(U < b) = \text{P}(V > c)$, where $b > 10$ and $c < 12$.
Determine $b$ in terms of $c$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2023 Q11 [9]}}