Estimating from Samples (Foundation): Fluency and Exam Drill - Worksheets, Questions and Revision

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F09D Estimating from Samples (Foundation): Fluency and Exam Drill

EDEXCEL 1ST0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A sample of 30 students found that 6 study French. Write down the fraction of the sample who study French.

(Total for Question 1 is 1 mark)

A sample of 40 shoppers found that 8 used a loyalty card. Write down the proportion of the sample who used a loyalty card, as a decimal.

(Total for Question 2 is 1 mark)

A sample of 5 boxes of nails contains these numbers of nails: 48, 52, 50, 49, 51. Write down the mean number of nails per box.

(Total for Question 3 is 1 mark)

A sample of 6 employees has these ages, in years: 22, 25, 30, 28, 24, 27. Write down the mean age, in years.

(Total for Question 4 is 1 mark)

A sample of 25 magazines in a shop found that 5 were sports magazines. Write down the proportion of the sample that were sports magazines, giving your answer as a fraction in its simplest form.

(Total for Question 5 is 1 mark)

A sample of 12 tomato plants had a mean yield of 15 tomatoes per plant. Write down the total number of tomatoes produced by the sample of 12 plants.

(Total for Question 6 is 1 mark)

Two samples are taken to estimate the mean height of a species of plant. Sample A has 10 plants. Sample B has 100 plants. Write down which sample is more likely to give a reliable estimate of the mean height.

(Total for Question 7 is 1 mark)

In a sample of 25 magazines, 5 are sports magazines. A shop has 400 magazines in total. Estimate the number of sports magazines in the shop.

(Total for Question 8 is 2 marks)

A sample of 20 packets of crisps has a mean mass of 32g. Estimate the total mass, in grams, of 250 packets like this.

(Total for Question 9 is 2 marks)

In a sample of 90 commuters, 63 travel to work by car. Work out the proportion of the sample who travel by car, giving your answer as a fraction in its simplest form.

(Total for Question 10 is 2 marks)

A factory samples 200 bulbs from a batch and finds that 8 are faulty. The batch contains 6000 bulbs in total. Estimate the number of faulty bulbs in the whole batch.

(Total for Question 11 is 2 marks)

A sample of 8 delivery vans had a mean of 45 parcels delivered per van in a day. Estimate the total number of parcels delivered by a fleet of 60 vans in a day.

(Total for Question 12 is 2 marks)

A biologist tags 25 fish in a pond, then releases them. She later catches a second sample of 40 fish, of which 5 are already tagged.

Capture-recapture formula:
estimated population = (number tagged in 1st catch x total in 2nd catch) / (number tagged in 2nd catch)

Use the formula to estimate the number of fish in the pond.

(Total for Question 13 is 2 marks)

A sample of 8 fish caught from a lake had the following masses, in grams: 340, 355, 350, 345, 360, 348, 352, 350. The lake is estimated to contain 2500 fish of this species.

Work out the mean mass of a fish in the sample, then use your answer to estimate the total mass, in grams, of all 2500 fish in the lake.

(Total for Question 14 is 3 marks)

A gym has 1800 members. A sample of 60 members found that 42 attended a class in the last month.

Work out the percentage of the sample who attended a class, and use this to estimate how many of the gym's 1800 members attended a class in the last month.

(Total for Question 15 is 3 marks)

A researcher wants to estimate what proportion of all residents in a town recycle regularly. She stands outside a recycling centre on a Saturday morning and surveys 50 people leaving it. 46 of them say they recycle regularly.

Explain why this sample is unlikely to give a reliable estimate for all town residents, and state whether the estimate is likely to be too high or too low.

(Total for Question 16 is 3 marks)

A ranger estimates there are 180 rabbits living in a field, using the capture-recapture method. In the first catch, the ranger tagged 30 rabbits before releasing them. In the second catch, 60 rabbits were caught in total.

Capture-recapture formula:
estimated population = (number tagged in 1st catch x total in 2nd catch) / (number tagged in 2nd catch)

(a)Work out how many of the 60 rabbits in the second catch were already tagged.(2)

(b)Write your answer to part (a) as a percentage of the second catch, giving your answer to 1 decimal place.(2)

(Total for Question 17 is 4 marks)

A student is estimating the number of left-handed pupils in a school of 900 pupils, using a sample of 40 pupils in which 6 are left-handed. Here is the student's working:

Proportion of left-handed pupils in the sample = 6/40 = 0.15
Estimated number of left-handed pupils in the school = 0.15 + 900 = 900.15

(a)Identify the error in the student's working.(1)

(b)Work out the correct estimate for the number of left-handed pupils in the school.(2)

(Total for Question 18 is 3 marks)

A conservation volunteer wants to estimate the number of bats roosting in a barn, using the capture-recapture method.

(a)Give one reason why it would not be practical for the volunteer to count every bat in the barn directly.(1)

(b)The volunteer catches and tags 18 bats one night, then releases them. Give one thing she should do before catching the second sample, to make sure the estimate is reliable.(1)

(c)A week later, she catches a second sample of 24 bats, of which 6 are already tagged. Use the capture-recapture method to estimate the number of bats roosting in the barn.(2)

(d)Give one assumption that must be true for this estimate of 72 to be reliable.(1)

(Total for Question 19 is 5 marks)

Mark scheme · F09D Estimating from Samples (Foundation): Fluency and Exam Drill

Question 1

B1 6/30 oe (1/5, 0.2) cao
Answer: 6/30 (= 1/5)

Question 2

B1 0.2 cao
Answer: 0.2

Question 3

B1 50 cao
Answer: 50

Question 4

B1 26 cao
Answer: 26

Question 5

B1 1/5 oe cao
Answer: 1/5

Question 6

B1 180 cao
Answer: 180

Question 7

B1 Sample B cao
Answer: Sample B

Question 8

M1 5/25 x 400, oe
A1 80 cao
Answer: 80

Question 9

M1 32 x 250, oe
A1 8000 cao
Answer: 8000 g

Question 10

M1 63/90, oe
A1 7/10 cao
Answer: 7/10

Question 11

M1 8/200 x 6000, oe
A1 240 cao
Answer: 240

Question 12

M1 45 x 60, oe
A1 2700 cao
Answer: 2700

Question 13

M1 25 x 40 (=1000), oe
A1 200 cao
Answer: 200

Question 14

M1 correct sum of the 8 masses (=2800), or equivalent
M1 2800/8 (=350), then multiplying their mean by 2500, oe
A1 875000 cao
Answer: 875,000 g (mean 350 g per fish)

Question 15

M1 42/60, oe (=0.7 or 70%)
M1 0.7 x 1800, oe
A1 1260 cao
Answer: 70%; an estimated 1260 members

Question 16

B1 identifies that the sample only includes people already at the recycling centre, who are more likely to recycle than a resident chosen at random, oe (bias identified)
B1 states the estimate is likely to be too high, oe
B1 explains that residents who do not visit the recycling centre (e.g. non-recyclers) are not represented in the sample, oe
Answer: The sample is biased because only recycling-centre visitors were asked; the estimate (92%) is likely too high because residents who do not recycle, or do not visit the centre, are not represented.

Question 17

(a) M1 180 = (30 x 60) / m, oe (correct equation set up for the unknown number tagged, m)
(a) A1 10 cao
(a) Answer: 10
(b) M1 10/60, oe (ft their answer to (a))
(b) A1 16.7% cao (awrt 16.7%)
(b) Answer: 16.7%

Question 18

(a) B1 the student added the proportion and 900 instead of multiplying them (should be 0.15 x 900, not 0.15 + 900), oe
(a) Answer: The student added instead of multiplied.
(b) M1 0.15 x 900, oe
(b) A1 135 cao
(b) Answer: 135

Question 19

(a) B1 bats move around and roost in hard-to-reach places, so counting every one directly would disturb them or be very difficult and unreliable, oe
(a) Answer: Bats are mobile and roost in hard-to-reach places, so a full direct count would be impractical.
(b) B1 wait long enough for the tagged bats to mix back thoroughly (and randomly) with the rest of the colony before the second catch, oe
(b) Answer: Allow enough time for the tagged bats to mix back randomly with the rest of the colony.
(c) M1 18 x 24 (=432), oe
(c) A1 72 cao
(c) Answer: 72
(d) B1 the bat population stayed the same between the two catches (no bats born, died, or moved in/out), or the tagged bats mixed back randomly with the rest of the colony, oe
(d) Answer: The bat population must stay unchanged between catches, and tagged bats must mix back in randomly.

Question 19

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Estimating from Samples (Foundation): Fluency and Exam Drill - Worksheets, Questions and Revision

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F09D Estimating from Samples (Foundation): Fluency and Exam Drill

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Question 19

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