Edexcel A-Level Mathematics A2 S2.1.2 Mean and Variance of Binomial and Poisson Distributions Questions

Practise finding and using the mean and variance of binomial and Poisson variables to answer expected-value and parameter questions.

Exam points

calculate E(X)=np and Var(X)=np(1-p) for binomial variables from given parameters
state the Poisson variance from its mean and use expected frequencies in tables

[Maximum number: 2]

A research student is investigating the number of children who are girls in families with 4 children.

The table below shows her results for 200 such families.

Table for Question Edexcel A-Level Mathematics A2 S2.1.2 Mean and Variance of Binomial and Poisson Distributions Questions question 1 — Edexcel A-Level Mathematics A2

The research student suggests that a binomial distribution with $p=\frac{1}{2}$ could be a suitable model for the number of children who are girls in a family of 4 children.

Use the data in the table to show that the probability that a child is a girl is 0.45

The research student uses the probability from part (b) to calculate a new set of expected frequencies, none of which are less than 5
The statistic $\sum \frac{(O-E)^{2}}{E}$ is evaluated and found to be 2.47

$[0 \times 15+] 1 \times 68+2 \times 69+3 \times 38+4 \times 10[=360]$ $\frac{360}{200 \times 4}=0.45$ *

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Edexcel A-Level Mathematics A2 S2.1.2 Mean and Variance of Binomial and Poisson Distributions Questions question 1