Answer:
74.64% probability that the distance is at most 100 m
93.57% probability that the distance is at most 200 m
18.93% probability that the distance is between 100 and 200m.
Explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:

In which
is the decay parameter.
The probability that x is lower or equal to a is given by:

Which has the following solution:

In this problem, we have that:

What is the probability that the distance is at most 100 m?

74.64% probability that the distance is at most 100 m
At most 200 m?

93.57% probability that the distance is at most 200 m
Between 100 and 200 m?
0.9357 - 0.7464 = 0.1893
18.93% probability that the distance is between 100 and 200m.