Challenging +1.2 This question requires understanding of normal approximation to Poisson (a Further Maths Statistics topic), applying continuity correction, using inverse normal tables, and solving a quadratic equation. While it involves multiple steps and the algebraic manipulation to get a quadratic in √λ is non-trivial, the individual techniques are standard for S2 level. The question guides students toward the solution method, making it moderately challenging but not requiring deep insight.
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 \(\lambda\).
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 $\lambda$.
\hfill \mbox{\textit{CAIE S2 2015 Q2 [5]}}