| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2022 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then perform other calculations |
| Difficulty | Standard +0.3 This question tests understanding of histogram construction (frequency density) and sampling variation. Part (a) is a straightforward calculation of frequency density given probability and sample size. Parts (b) and (c) test conceptual understanding of why probabilities are needed for histogram heights and why sample variation is expected. These are standard A-level statistics concepts requiring minimal problem-solving beyond applying definitions. |
| Spec | 2.02b Histogram: area represents frequency2.02i Select/critique data presentation |
| \(X\) | \(256 \leqslant x < 259\) | \(259 \leqslant x < 262\) | \(262 \leqslant x < 265\) | \(265 \leqslant x < 267\) | \(267 \leqslant x < 300\) |
| Probability | 0.05 | 0.25 | 0.45 | 0.20 | 0.05 |
The probability distribution for $X$, the lifetime of a light bulb, in hours, is given below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$X$ & $256 \leqslant x < 259$ & $259 \leqslant x < 262$ & $262 \leqslant x < 265$ & $265 \leqslant x < 267$ & $267 \leqslant x < 300$ \\
\hline
Probability & 0.05 & 0.25 & 0.45 & 0.20 & 0.05 \\
\hline
\end{tabular}
\end{center}
a) Suppose that a random sample of 40 light bulbs is tested, and a histogram is drawn of their lifetimes. Calculate the expected height of the bar for the interval $262 \leqslant x < 265$.\\
b) Now suppose that the last two intervals are changed to $265 \leqslant x < 268$ and $268 \leqslant x < 300$. Explain why it is not possible to tell what will happen to the expected heights of the last two bars.\\
c) Celyn collects a different random sample of 40 light bulbs to test. She draws a histogram of their lifetimes and finds that it is different to the histogram referred to in part (a). Should Celyn be concerned that the two histograms are different?
\hfill \mbox{\textit{WJEC Unit 2 2022 Q2}}