The Binomial and Poisson distributions

Sample questions

Original practice questions written in the style of the exam.

1. Question 15 marks

   Calls arrive at a help desk at random at a mean rate of 3 every 10 minutes.

   (a) Find the probability that exactly 4 calls arrive in a 10-minute period.

   (b) Find the probability that more than 8 calls arrive in a 30-minute period.

   [You may use $P(Y \le 8) = 0.4557$ for $Y \sim \text{Po}(9)$.]

   Mark scheme

   • (a) M1 $P(X = 4) = \dfrac{e^{-3}3^4}{4!}$ (1)
2. Question 25 marks

   2% of the light bulbs made in a factory are faulty. A box contains 200 bulbs, and faults occur independently.

   (a) State the exact distribution of $X$, the number of faulty bulbs in the box.

   (b) Explain why a Poisson distribution is a suitable approximation, and state its parameter.

   (c) Use the approximation to find $P(X < 3)$.

   [You may use $P(Y \le 2) = 0.2381$ and for .]