- Customers in a shop have to queue to pay.
The partially completed table below and partially completed histogram opposite, give information about the time, \(x\) minutes, spent in the queue by each of 112 customers one day.
| Time in queue ( \(\boldsymbol { x }\) minutes) | Frequency |
| \(1 - 2\) | 64 |
| \(2 - 3\) | |
| \(3 - 4\) | 13 |
| \(4 - 6\) | |
| \(6 - 8\) | 3 |
No customer spent less than 1 minute or longer than 8 minutes in the queue.
- Complete the table.
- Complete the histogram.
Ting decides to model the frequency density for these 112 customers by a curve with equation
$$y = \frac { k } { x ^ { 2 } } \quad 1 \leqslant x \leqslant 8$$
where \(k\) is a constant.
- Find the value of \(k\)
\includegraphics[max width=\textwidth, alt={}]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-07_1584_1189_285_443}
Only use this grid if you need to redraw your histogram.
\includegraphics[max width=\textwidth, alt={}, center]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-09_1582_1192_367_440}
\includegraphics[max width=\textwidth, alt={}, center]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-09_2267_51_307_36}