In a particular survey involving 7076 households, 0.0248% were in favour of amending city council by-laws. The number in favour is to be modelled by a Poisson approximation to the binomial.

Find the mean of that Poisson distribution.

Model answer

1.75

Also accepted: 1,75, 1.8, 1,8, 1.755, 1,755, 1.7548, 1,7548

Explanation

A percentage of $0,0248\%$ is a probability of $p=0,000248$ , and the number of households surveyed is $n=7076$ .

The Poisson approximation to $B(n;\,p)$ uses the same mean as the binomial:

$\lambda=np=7076\times 0,000248=1,7548$ .

Derived from ZIMSEC Statistics Paper 4, June 2010, Q2

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