CAIE A-Level Mathematics A2 6.1.4 Binomial Distribution Questions

Practise replacing a binomial model by Po(np) when trials are numerous and success is rare, justifying the choice and evaluating exact or cumulative probabilities.

[Maximum number: 4]

The random variable X has the distribution B(4000,0.001).

(a)

Use a suitable approximating distribution to find $\mathrm{P}(2 \leqslant X<5)$ .

[ 3 ]

[ $\lambda=$ ] 4
$\mathrm{e}^{-4}\left(\frac{4^{2}}{2!}+\frac{4^{3}}{3!}+\frac{4^{4}}{4!}\right)$

or $\mathrm{e}^{-4}(8+10.67+10.67)$

or 0.1465+0.19537+0.19537
Marking guidance:

Allow one end error.

Any $\lambda$ .

Expression must be seen.

=0.537(3 sf)
SC B1 B1 for unsupported correct answer.

SC B2 for use of Binomial leading to 0.537.

Note: use of normal could score B1 only for mean =4.

(b)

Justify your approximating distribution in this case.

[ 1 ]

All question bank results loaded

CAIE A-Level Mathematics A2 6.1.4 Binomial Distribution Questions question 1

Question (a)

Question (b)