Sampling and populations

Maria wants to find an estimate for the number of frogs in a lake. On Saturday she catches 40 of the frogs. She puts a tag on each frog and releases them. On Monday she catches 55 of the frogs. 11 of the frogs have tags.

Work out an estimate for the total number of frogs in the lake. You must show all your working.

State one assumption you have made.

A car factory is going to make four different car models A, B, C and D. 80 people are asked which of the four models they would be most likely to buy. The table shows information about the results.

The factory is going to make 40 000 cars next year. Work out how many model B cars the factory should make next year.

A car factory is going to make four different car models A, B, C and D. 80 people are asked which of the four models they would be most likely to buy. The table shows information about the results.

The factory is going to make 40 000 cars next year. Work out how many model B cars the factory should make next year.

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.

Find an estimate for the number of rabbits in the park.

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.

Explain why Albie’s estimate cannot be correct.

Saffron wants to work out an estimate for the total number of fish in a lake. On Friday, Saffron catches 180 fish from the lake. She puts a tag on each of these fish and puts them back into the lake. On Saturday, Saffron catches 305 fish from the same lake. She finds that 45 of the 305 fish are tagged. Work out an estimate for the total number of fish in the lake.

Shirley wants to find an estimate for the number of bees in her hive. On Monday she catches 90 of the bees. She puts a mark on each bee and returns them to her hive. On Tuesday she catches 120 of the bees. She finds that 20 of these bees have been marked.

Work out an estimate for the total number of bees in her hive.

Shirley assumes that none of the marks had rubbed off between Monday and Tuesday.

If Shirley’s assumption is wrong, explain what effect this would have on your answer to part (a).

Each person in a fitness club is going to get a free gift. Stan is going to order the gifts.

Stan takes a sample of 50 people in the fitness club. He asks each person to tell him the gift they would like.

The table shows information about his results.

There are 700 people in the fitness club.

Work out how many sports bags Stan should order.

Write down any assumption you made and explain how this could affect your answer.

Hannah is planning a day trip for 195 students. She asks a sample of 30 students where they want to go. Each student chooses one place. The table shows information about her results.

Work out how many of the 195 students you think will want to go to the Theme Park.

State any assumption you made and explain how this may affect your answer.

Hannah is planning a day trip for 195 students. She asks a sample of 30 students where they want to go. Each student chooses one place. The table shows information about her results.

Work out how many of the 195 students you think will want to go to the Theme Park.

State any assumption you made and explain how this may affect your answer.