Question 6 - A-Level Maths

Exam Board	Edexcel
Module	S2 (Statistics 2)
Year	2016
Session	October
Topic	Poisson Distribution
Type	Poisson parameter from given probability

According to an electric company, power failures occur randomly at a rate of \(\lambda\) every 10 weeks, \(1 < \lambda < 10\)
1. Write down an expression in terms of \(\lambda\) for the probability that there are fewer than 2 power failures in a randomly selected 10 week period.
2. Write down an expression in terms of \(\lambda\) for the probability that there is exactly 1 power failure in a randomly selected 5 week period.
Over a 100 week period, the probability, using a normal approximation, that fewer than 15 power failures occur is 0.0179 (to 3 significant figures).
1. Justify the use of a normal approximation.
2. Find the value of \(\lambda\). Show each stage of your working clearly.