Higher November 2024 Paper 5 Q17
17 A farmer grows pumpkins.
The farmer records the masses, \(m\) kilograms, of 80 of their pumpkins.
The table shows the results.
| Mass (\(m\) kg) | \(0 \lt m \leqslant 5\) | \(5 \lt m \leqslant 10\) | \(10 \lt m \leqslant 15\) | \(15 \lt m \leqslant 20\) | \(20 \lt m \leqslant 25\) |
|---|---|---|---|---|---|
| Frequency | 10 | 22 | 28 | 14 | 6 |
(a) Complete the cumulative frequency table.
| Mass (\(m\) kg) | \(m \leqslant 5\) | \(m \leqslant 10\) | \(m \leqslant 15\) | \(m \leqslant 20\) | \(m \leqslant 25\) |
|---|---|---|---|---|---|
| Cumulative frequency | 10 | 32 |
[1]
(b) Draw the cumulative frequency graph to represent these results. [3]
(c) Write down the upper quartile of the mass of the 80 pumpkins. [1]
(d) The farmer picks a pumpkin at random.
Find an estimate for the probability that the pumpkin has a mass greater than 18 kg. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 60, 74, 80 | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Correct curve | 3 | B1 for correct horizontal plots B1FT for correct vertical plots B1FT their (a) for smooth increasing curve through 5 points | Condone polygon, ignore curve to left of \(m = 5\) Accuracy ½ small sq radially on curve and plots Condone increasing linear graph Ignore blocks |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 15 | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Strict FT their curve \(\frac{80 - \textit{their} \text{ reading at 18 kg}}{80}\) oe | 2 | B1 for 80 – their reading at 18 kg or \(\frac{\textit{their} \text{ reading at 18 kg}}{80}\) | For 2 marks, accept fract/dec/% equivalents isw cancelling/conversion Accept FT polygon for curve For 2 marks or B1 accept their reading ± 1 |