Well, I'm not quite sure if I'm right (haven't got any statistic books in front of me to check it out), but lets try anyway.

Given this information, we can conclude that the probability that 0 are going to be sick is 11,603%, that 1 is going to be sick is 31,239%, that 2 are going to be sick is 33,642%, that 3 are going to be sick is 18,115%, that 4 are going to be sick is 4,877% and that 5 are going to be sick is 0,525%.

Now, consider the following two scenarios.

1) If we build two beds then:

- Expected travel cost if 3 are sick (means that 1 is going to the hospital) is going to be 1*18,115%*600 = 108,6881.
- Expected travel cost if 4 are sick (means that 2 are going to the hospital) is going to be 2*4,877%*600 = 58,524.
- Expected travel cost if 5 are sick (means that 3 are going to the hospital) is going to be 3*0,525%*600 = 9,4539.

The sum of this plus the daily cost of running the two bed clinic will then equal to 576,67.

2) If we build three beds then:

- Expected travel cost if 4 are sick is 29,26
- Expected travel cost if 5 are sick is 6,30.

The sum of this plus the daily cost of running the three bed clinic will then equal to 605,56.

Hence, it is cheaper to build just the two bed clinic.

But again, I'm not 100% sure about this.