Moderate -0.3 This is a straightforward application of the normal approximation to the Poisson distribution. Students need to recognize when to use the approximation (large λ), apply continuity correction, standardize to find P(X > 60), and use normal tables. While it requires multiple steps, each is routine for S2 level with no conceptual challenges or novel problem-solving required.
2 The number of enquiries received per day at a customer service desk has a Poisson distribution with mean 45.2. If more than 60 enquiries are received in a day, the customer service desk cannot deal with them all.
Use a suitable approximating distribution to find the probability that, on a randomly chosen day, the customer service desk cannot deal with all the enquiries that are received.
2 The number of enquiries received per day at a customer service desk has a Poisson distribution with mean 45.2. If more than 60 enquiries are received in a day, the customer service desk cannot deal with them all.
Use a suitable approximating distribution to find the probability that, on a randomly chosen day, the customer service desk cannot deal with all the enquiries that are received.\\
\hfill \mbox{\textit{CAIE S2 2021 Q2 [4]}}