Normal approximation to the binomial and PoissonEdexcel International A Level Further Maths: Mind map

Exam questions on Normal approximation to the binomial and Poisson

1. The random variable $X$ has distribution $\mathrm{B}(80,0.4)$, and a normal approximation is to be used.
   Hence calculate an approximation to $\mathrm{P}(X\le30)$.2 marks
2. The number of emails $X$ received by a help desk in one hour has distribution $\mathrm{Po}(25)$, and a normal approximation is to be used.
   Hence calculate an approximation to $\mathrm{P}(X\ge30)$.2 marks
3. A component is defective with probability $0.45$, independently of other components. In a random sample of $150$ components, $X$ is the number that are defective.
   Using a suitable normal approximation, find $\mathrm{P}(X=70)$.3 marks