CAIE S2 2015 November — Question 2

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2015
SessionNovember
TopicApproximating the Poisson to the Normal distribution
TypeFind parameter from given probability

2 The number of calls received per 5-minute period at a large call centre has a Poisson distribution with mean \(\lambda\), where \(\lambda > 30\). If more than 55 calls are received in a 5 -minute period, the call centre is overloaded. It has been found that the probability of being overloaded during a randomly chosen 5 -minute period is 0.01 . Use the normal approximation to the Poisson distribution to obtain a quadratic equation in \(\sqrt { } \lambda\) and hence find the value of \(\lambda\).