The number of clients who arrive at an information desk has a Poisson distribution with mean 2.2 per 5-minute period.

1. (a)Find the probability that, in a randomly chosen 15-minute period, exactly 6 clients arrive at the desk.[3]
2. (b)If more than 4 clients arrive during a 5-minute period, they cannot all be served. Find the probability that, during a randomly chosen 5-minute period, not all the clients who arrive at the desk can be served.[2]
3. (c)Use a suitable approximating distribution to find the probability that, during a randomly chosen 1-hour period, fewer than 20 clients arrive at the desk.[4]