It has been 20+ years since I have had to breakout the AP stats knowledge, and I have hit a huge brick wall! Thus far my search for stats help has come up empty, so I am praying someone here can help me solve my problem.

We receive 9 different types of calls in a given month. Some call types occur more frequently than others. We are evaluating two different call centers on their effectiveness at resolving customers issues. Each call type that comes in is scored on a scale of 1 to 100, with 1 being utterly ineffective at customer resolution and 100 being a perfect customer resolution. We have a sample size of 30 calls for each of the 9 different call types for each center (30*9*2 = 540 samples), for which we can calculate the mean and standard deviation for each call type for each Center, thus allowing us to calculate the probability that Center A is better than Center B. (I am using the NORM.DIST function in excel to find the probability that Center A is better than Center B)

What I need to know is: For a random call, what is the overall probability that Center A is better than Center B?

Example data

- Call type 1 - 12% of monthly Call Volume - 88% probability Center A is better than Center B
- Call type 2 - 01% of monthly Call Volume - 32% probability Center A is better than Center B
- Call type 3 - 02% of monthly Call Volume - 60% probability Center A is better than Center B
- Call type 4 - 22% of monthly Call Volume - 75% probability Center A is better than Center B
- Call type 5 - 22% of monthly Call Volume - 82% probability Center A is better than Center B
- Call type 6 - 14% of monthly Call Volume - 62% probability Center A is better than Center B
- Call type 7 - 06% of monthly Call Volume - 61% probability Center A is better than Center B
- Call type 8 - 16% of monthly Call Volume - 71% probability Center A is better than Center B
- Call type 9 - 05% of monthly Call Volume - 42% probability Center A is better than Center B