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# Binomial or Not?

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Age 16 to 18

Challenge Level

Which of these situations could be modelled using the binomial distribution?

For those which can be modelled by the binomial distribution $\mathrm{B}(n,p)$, what are "success" and "failure", and what are $n$ and $p$?

For those which are not, why not? Is there something small you could change that would make the binomial distribution appropriate? Is the binomial distribution at least a good approximation in this situation?

*This resource is part of the collection Statistics - Maths of Real Life*

For those which can be modelled by the binomial distribution $\mathrm{B}(n,p)$, what are "success" and "failure", and what are $n$ and $p$?

For those which are not, why not? Is there something small you could change that would make the binomial distribution appropriate? Is the binomial distribution at least a good approximation in this situation?

- A bag contains red, green and blue balls. 10 balls are taken at random, one at a time. Each ball's colour is recorded, and then returned to the bag.

- A coin is flipped until a tail is obtained. The total number of flips needed is recorded.

- The number of rainy days in April in the village of Springfield is recorded.

- The children in a class each do the same mathematics test. The number who score above 80% is recorded.

- Five fair coins are stuck to a piece of clear plastic. The plastic is flipped in the air, and the number of heads showing when the plastic lands is recorded.

- A person plays a lottery every week. They record the number of times they win a prize during one year.

- A cancer drug is being tested. 1000 patients are given the drug, and the number of patients who die within five years is recorded.

- A basketball player is practising taking shots. The number of successful shots out of 10 attempts is recorded.

- A bag contains red and blue balls. 10 balls are taken at random, one at a time. Each ball's colour is recorded, and then returned to the bag.

- A box of pens contains working pens and broken pens. 10 pens are taken together from the box at random, and the number of working pens is recorded.

- A bag contains red, green and blue balls. 10 balls are taken from the bag at random one at a time, and replaced immediately. The number of green balls taken is recorded.

- A farmer is planting a crop. On average, a certain percentage of the seeds grow to maturity. The number of seeds that grow to maturity in this field in this year is recorded.