(a)[3]
Determine the probability that, in a randomly selected $15$-minute interval, exactly $6$ clients reach the desk.
(b)[2]
If more than $4$ clients arrive in a $5$-minute interval, they all cannot be served. Find the probability that, in a randomly chosen $5$-minute interval, the arriving clients at the desk cannot all be served.
(c)[4]
Use an appropriate approximating distribution to find the probability that, in a randomly selected $1$-hour interval, fewer than $20$ clients arrive at the desk.