Higher November 2022 Paper 2 Q15
15 Faiza is studying the population of rabbits in a park.
She wants to estimate the number of rabbits in the park.
On Monday she catches a random sample of 20 rabbits in the park, marks each rabbit with a tag and releases them back into the park.
On Tuesday she catches a random sample of 42 rabbits in the park.
12 of the rabbits are marked with a tag.
(a) Find an estimate for the number of rabbits in the park. (3)
Albie is studying the population of rabbits in a wood.
One day, he catches 55 rabbits and finds that 40 of these rabbits are marked with a tag.
Albie estimates there are 50 rabbits in the wood.
(b) Explain why Albie’s estimate cannot be correct. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 70 | P1 | for \(\dfrac{20}{12}\ (= 1.66..)\) or \(\dfrac{12}{20}\ (= 0.6)\) or \(\dfrac{12}{42}\ (= 0.2857..)\) or \(\dfrac{42}{12}\ (= 3.5)\) |
| P1 | for \(\dfrac{20}{n} = \dfrac{12}{42}\) or \(\dfrac{12}{20} = \dfrac{42}{n}\) or \(\dfrac{20 \times 42}{12}\) | |
| A1 | cao |
Additional guidance
Decimal values truncated or rounded to 2 dp or more
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | C1 | for explanation Acceptable examples the sample size cannot be greater than the population the population is greater than the sample size there are more than 50 rabbits he catches 55 rabbits Not acceptable examples the sample size is too small some of the tags could fall off he has underestimated |