Edexcel A-Level Mathematics A2 S2.1.3 The Questions

Practise replacing suitable binomial models with Poisson approximations and calculating rare-event probabilities from verified Edexcel IAL questions.

Exam points

convert B(n,p) to Po(np) when n is large and p is small, then calculate a tail probability

[Maximum number: 3]

The length of pregnancy for a randomly selected pregnant sheep is D days where

D \sim \mathrm{~N}\left(112.4, \sigma^{2}\right)

Given that 5% of pregnant sheep have a length of pregnancy of less than 108 days,

Charlie takes 200 random samples of 25 pregnant sheep.

Use a Poisson approximation to estimate the probability that at least 2 of the samples have more than 3 pregnant sheep with a length of pregnancy of less than 108 days.

$T\sim \operatorname{Po}(200\times0.0341)=\operatorname{Po}(6.82)$ $\mathrm{P}(T>2)=1-\mathrm{P}(T\le 1)$ $=1-(\mathrm{e}^{-6.82}+\mathrm{e}^{-6.82}\times6.82)$ $=0.99146\ldots\quad(\text{calc }0.99144\ldots)$

All question bank results loaded

Edexcel A-Level Mathematics A2 S2.1.3 The Questions question 1