- In a village shop the customers must join a queue to pay. The number of customers joining the queue in a 10 minute interval is modelled by a Poisson distribution with mean 3
Find the probability that
- exactly 4 customers join the queue in the next 10 minutes,
- more than 10 customers join the queue in the next 20 minutes.
When a customer reaches the front of the queue the customer pays the assistant. The time each customer takes paying the assistant, \(T\) minutes, has a continuous uniform distribution over the interval \([ 0,5 ]\). The random variable \(T\) is independent of the number of people joining the queue.
- Find \(\mathrm { P } ( T > 3.5 )\)
In a random sample of 5 customers, the random variable \(C\) represents the number of customers who took more than 3.5 minutes paying the assistant.
- Find \(\mathrm { P } ( C \geqslant 3 )\)
Bethan has just reached the front of the queue and starts paying the assistant.
- Find the probability that in the next 4 minutes Bethan finishes paying the assistant and no other customers join the queue.