Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer between a "worker" computer and a "master" computer. Suppose that X has a gamma distribution with mean value 37.5 ms and standard deviation 21.6 (suggested by the article "Computation Time of Grid Computing with Data Transfer Times that Follow a Gamma Distribution," Proceedings of the First International Conference on Semantics, Knowledge, and Grid, 2005).
a. What are the values of a and b?
b. What is the probability that data transfer time exceeds 50 ms?
c. What is the probability that data transfer time is between 50 and 75 ms?