An upper level disturbance will be crossing the Illinois/Indiana area Friday night, and thunderstorms are likely to occur during the overnight hours. There is a small chance that some showers could linger around Speedway after sunrise, but they should be gone by the time of the first on-track session (Xfinity practice) at 9:35 am EDT. The rest of Saturday should be dry and mostly sunny, with temperatures reaching into the mid 80s. There could be a few showers in the area Saturday evening as a front moves into the area, after the end of the Xfinity Pennzoil 150.
Another upper level disturbance will cross the Mississippi River on Sunday, and track east through the afternoon. Showers with this system are expected to move into central Indiana late in the day or during the evening, most likely after the end of the Verizon 200. If the timing of this system shifts a little earlier, it could impact the late stages of the race, but I think the chance of that happening is low.