Find parameter from given probability

A question is this type if and only if it requires finding the value of λ (or related parameter) given a probability statement, typically involving solving an equation using normal approximation.

2 questions

CAIE S2 2015 November Q2
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 \(\lambda\).
Edexcel S2 2018 June Q5
5. Cars stop at a service station randomly at a rate of 3 every 5 minutes.
  1. Calculate the probability that in a randomly selected 10 minute period,
    1. exactly 7 cars will stop at the service station,
    2. more than 7 cars will stop at the service station. Using a normal approximation, the probability that more than 40 cars will stop at the service station during a randomly selected \(n\) minute period is 0.2266 correct to 4 significant figures.
  2. Find the value of \(n\).