An airport counter checks in an average of 4 guests every 10 minutes.

a. What is the probability that between 5:45 pm and 6:30 pm, exactly 10 guests arrive with six of them arriving within the first 30 minutes, and the rest arriving within the last 15 minutes?

b. Suppose that a guest was just served now. There is a 60% chance that the next guest will arrive in x minutes or more. What is the value of x?

c. Assume that the airport implements a mandatory rest break for counter staff after they have served 50 guests. Find the mean and standard deviation of the number of hours a counter staff will have to work before being forced to take a break.