Although it has been wet, a quick look at the weather records suggests that the area has seen wetter. Let's start with the Salt Lake City International Airport. Through yesterday, the accumulation for August 1–27 was 1.77 inches (green line), well above average (brown line). That ties it for 8th amongst the wettest August 1–27 periods. However, there have been similar periods in past years that were much wetter, including 1968 when 3.66 inches fell (blue line).
Alta has been deluged this August with an accumulation of 5.33" so far, which puts it just behind 1983 (5.97"). There is some missing data for the period though (black dots), including yesterday, which will add to the total. On the other hand, the data at this location is very spotty. For instance, there is no data for August 1–27, 1968, which was the wettest such period at some nearby stations. Thus, we can't make any definitive conclusions here, but we can say it's certainly been very wet.
Finally, if we go down to Utah County, records from the school that shall not be named show August 1–27 to be wet with 2.54", but not record setting. Here, long-term records are also spotty (1968 is missing, for example).
I suspect if we had a dense and complete precipitation observing network covering 50 years we would find that August 1–27, 2014 ranks in the top 10 such periods at most locations in the Salt Lake area and perhaps near record levels at a few spots that have really gotten walloped by the thunderstorms. During the past 50 years, August 1–27, 1968 may be the wettest such period on record, although I've only looked at a few stations and there could be some exceptions to this given the hit-and-miss nature of monsoon thunderstorms.
If you are interested in records for the month, we still have 4 days left. Although there are no big monsoon surges in the offing, we have a chance of some showers and thunderstorms later today and perhaps we'll see something pop up later in the period. Some sites could add to their totals.