Choosing a distribution and approximationsEdexcel A-Level Maths: Flashcards

What these 14 flashcards ask

Four conditions for a binomial model?
Give a situation where independence may fail.
Why does sampling without replacement from a small population break the binomial model?
How can a sample be chosen so that a binomial model is more suitable?
When is a Normal model suitable?
Name a feature that makes a Normal model unsuitable.
When can B(n,p) be approximated by a Normal distribution?
What is the Normal approximation to B(n,p)?
Approximate B(60,0.45) by a Normal distribution.
Why is a continuity correction needed?
P(X\ge30) becomes what in the Normal approximation?
P(X<20) becomes what in the Normal approximation?
P(a\le X\le b) becomes what in the Normal approximation?
Why is the approximation poor for B(50,0.05)?

Exam questions on Choosing a distribution and approximations

Each seed in a very large batch germinates independently with probability 0.45. A random sample of 60 seeds is planted and $X$ is the number that germinate.
Use a Normal approximation to estimate $P(X\ge30)$ .2 marks
A school has many students, of whom 10% walk to school. A researcher selects the 25 students in one tutor group and records $X$ , the number who walk to school. Students in the same tutor group often live in the same roads.
Suggest how the researcher could choose the sample so that a binomial model would be more suitable.2 marks
A biased coin has probability 0.55 of landing heads. It is tossed 80 times and $H$ is the number of heads.
Explain why $H$ can be modelled by a Normal distribution, and state the distribution that should be used.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).