Calculate multiple probabilities using Poisson approximation

Questions that require calculating two or more different probability values in separate parts (e.g., both P(X<a) and P(X=b)) using Poisson approximation to the binomial.

1 questions

CAIE S2 2021 March Q4
4 On average, 1 in 400 microchips made at a certain factory are faulty. The number of faulty microchips in a random sample of 1000 is denoted by \(X\).
  1. State the distribution of \(X\), giving the values of any parameters.
  2. State an approximating distribution for \(X\), giving the values of any parameters.
  3. Use this approximating distribution to find each of the following.
    1. \(\mathrm { P } ( X = 4 )\).
    2. \(\mathrm { P } ( 2 \leqslant X \leqslant 4 )\).
  4. Use a suitable approximating distribution to find the probability that, in a random sample of 700 microchips, there will be at least 1 faulty one.