| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2011 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Single sum threshold probability |
| Difficulty | Standard +0.3 This is a straightforward application of standard results for sums of independent normal random variables. Part (a) requires recall of formulas (mean multiplies by n, SD multiplies by √n). Parts (b) and (c) involve routine normal probability calculations with no conceptual challenges—students simply set up the linear combination, find its distribution parameters, and use tables. The multi-step nature and 10 total marks place it slightly above average, but it requires no novel insight or problem-solving beyond textbook exercises. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.04b Linear combinations: of normal distributions |
The lifetimes of batteries from manufacturer $A$ are normally distributed with mean 20 hours and standard deviation 5 hours when used in a camera.
\begin{enumerate}[label=(\alph*)]
\item Find the mean and standard deviation of the total lifetime of a pack of 6 batteries from manufacturer $A$.
[2]
\end{enumerate}
Judy uses a camera that takes one battery at a time. She takes a pack of 6 batteries from manufacturer $A$ to use in her camera on holiday.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the probability that the batteries will last for more than 110 hours on her holiday.
[2]
\end{enumerate}
The lifetimes of batteries from manufacturer $B$ are normally distributed with mean 35 hours and standard deviation 8 hours when used in a camera.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the probability that the total lifetime of a pack of 6 batteries from manufacturer $A$ is more than 4 times the lifetime of a single battery from manufacturer $B$ when used in a camera.
[6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2011 Q6 [10]}}