| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Expected frequency with unknown parameter |
| Difficulty | Moderate -0.3 This is a straightforward S1 normal distribution question requiring standard z-score calculations and inverse normal work to find an unknown parameter. Part (c) involves finding σ from a given probability, which is slightly beyond pure recall but still routine for S1. The question is slightly easier than average A-level due to being from S1 (a less demanding module) with clear structure and standard techniques throughout. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
8. The lifetimes of bulbs used in a lamp are normally distributed.
A company $X$ sells bulbs with a mean lifetime of 850 hours and a standard deviation of 50 hours.
\begin{enumerate}[label=(\alph*)]
\item Find the probability of a bulb, from company $X$, having a lifetime of less than 830 hours.
\item In a box of 500 bulbs, from company $X$, find the expected number having a lifetime of less than 830 hours.
A rival company $Y$ sells bulbs with a mean lifetime of 860 hours and $20 \%$ of these bulbs have a lifetime of less than 818 hours.
\item Find the standard deviation of the lifetimes of bulbs from company $Y$.
Both companies sell the bulbs for the same price.
\item State which company you would recommend. Give reasons for your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2009 Q8 [11]}}