| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Single sum threshold probability |
| Difficulty | Standard +0.3 This is a straightforward application of sampling distribution theory and linear combinations of normal variables. Parts (a) and (b) are standard textbook exercises on sampling distributions (mean and standard error of sample mean). Part (c) requires combining two normal distributions (6M + 4F) and finding a probability, which is routine S3 content requiring no novel insight—just careful arithmetic with the formula for variance of linear combinations. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.04b Linear combinations: of normal distributions |
The weights of a group of males are normally distributed with mean 80 kg and standard deviation 2.6 kg. A random sample of 10 of these males is selected.
\begin{enumerate}[label=(\alph*)]
\item Write down the distribution of $M$, the mean weight, in kg, of this sample. [2]
\item Find P($M < 78.5$). [3]
\end{enumerate}
The weights of a group of females are normally distributed with mean 59 kg and standard deviation 1.9 kg. A random sample of 6 of the males and 4 of the females enters a lift that can carry a maximum load of 730 kg.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item Find the probability that the maximum load will be exceeded when these 10 people enter the lift. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 Q3 [10]}}