CAIE A-Level Mathematics A2 6.1.5 Normal Distribution Questions

Practise approximating Po(λ) by N(λ, λ) when the mean is large, applying half-unit continuity corrections and standardising with standard deviation √λ.

[Maximum number: 5]

A random variable X has the distribution Po(145).

(a)

Use a suitable approximating distribution to calculate $\mathrm{P}(X \leqslant 150)$ .

[ 4 ]

N(145, 145)
Stated or implied.

$\pm \frac{150.5-145}{\sqrt{145}}$ $[= \pm 0.457]$
Condone incorrect or omitted continuity correction.

$\Phi$ ('0.457')
For area consistent with their working.

=0.676(3 sf)
SC: Unsupported answer of 0.676 scores B3. Unsupported answer of 0.646 or 0.661 scores B2. Unsupported answer of 0.6799 scores B1.

(b)

Justify the use of your approximating distribution in this case.

[ 1 ]

145>15
Explicit. $\lambda>15$ B0 if $\lambda=145$ not stated. Accept $\geqslant$ Accept mean for $\lambda$ .

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CAIE A-Level Mathematics A2 6.1.5 Normal Distribution Questions question 1

Question (a)

Question (b)