Edexcel A-Level Mathematics A2 S2.1.1 Binomial and Poisson Distributions Questions

Build and test binomial and Poisson models, calculate exact or cumulative probabilities, and judge model suitability using verified Edexcel IAL questions.

Exam points

calculate exact and cumulative count probabilities using binomial or Poisson formulae
decide when a Poisson model is suitable by comparing the sample mean and variance
form a second-stage binomial model when repeated samples meet a stated condition

[Maximum number: 2]

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,

Qiang selects 25 pregnant sheep at random from a large flock.

Find the probability that more than 3 of these pregnant sheep have a length of pregnancy of less than 108 days.

$J\sim\mathrm{B}(25,0.05)$ $[\mathrm{P}(J\geq4)=]1-\mathrm{P}(J\leq3)=1-0.9659$ =0.0341 (calc $0.034090\ldots$ )

awrt 0.0341
(2)

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Edexcel A-Level Mathematics A2 S2.1.1 Binomial and Poisson Distributions Questions question 1