| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2002 |
| 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 sampling distributions and linear combinations of normal variables. Part (a) requires recalling that the sample mean follows N(μ, σ²/n). Part (b) is a routine normal probability calculation. Part (c) involves combining independent normal variables (6M + 4F), which is a textbook application requiring no novel insight—just careful arithmetic with means and variances. Slightly above average difficulty due to the multi-step nature and potential for arithmetic errors, but well within standard S3 material. |
| 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 $\bar{M}$, the mean weight, in kg, of this sample. [2]
\item Find P($\bar{M} < 78.5$). [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{enumi}{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 2002 Q3 [10]}}