6 Customers arrive at a post office at a constant average rate of 0.4 per minute.
- State an assumption needed to model the number of customers arriving in a given time interval by a Poisson distribution.
Assuming that the use of a Poisson distribution is justified,
- find the probability that more than 2 customers arrive in a randomly chosen 1 -minute interval,
- use a suitable approximation to calculate the probability that more than 55 customers arrive in a given two-hour interval,
- calculate the smallest time for which the probability that no customers arrive in that time is less than 0.02 , giving your answer to the nearest second.