Pearson Edexcel IAL Mathematics S2.3.2 Normal approximation to the binomial distribution

Practise using normal approximations to binomial or Poisson counts, with continuity corrections, standardisation and parameter recovery.

Exam points

write the approximating normal model with mean and variance from binomial or Poisson data
use standardised probability equations to solve for n, p, μ, σ or an unknown length

[Maximum number: 3]

In a peat bog, Common Spotted-orchids occur at a mean rate of 4.5 per $\mathrm{m}^{2}$

Assuming that in the peat bog, Common Spotted-orchids still occur at a mean rate of 4.5 per m^2

use a normal approximation to find the probability that in a randomly selected 20 m^2 of the peat bog there are fewer than 70 Common Spotted-orchids.

$T \sim \mathrm{~N}(90,90)$

B1

$\mathrm{P}(T<70)=\mathrm{P}\left(Z< \pm\left(\frac{69.5-90}{\sqrt{90}}\right)\right) \text { or } \mathrm{P}(Z< \pm 2.160 \ldots \ldots)$
=0.0154

awrt 0.0154

A1

(3)

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S2.3.2 - Normal approximation to the binomial distribution question 1