Practise approximating Po(λ) by N(λ, λ) when the mean is large, applying half-unit continuity corrections and standardising with standard deviation √λ.
The number, X, of books received at a charity shop has a constant mean of 5.1 per day.
Use a suitable approximating distribution to find the probability that more than 180 books are received in a 30-day period.
The number of DVDs received at the same shop is modelled by an independent Poisson distribution with mean 2.5 per day.
N(153, 153)
B1
Seen or implied.
180.5-153153 [=2.223]
M1
For standardising with their values (can be implied).
Allow with wrong or missing continuity correction.
1- ('2.223')
M1
For correct probability area consistent with their values.
=0.0131(3 sf)
A1