Is "normal distribution" a good choice for modeling future inflation rates?
With many financial variables you can deduce the distribution from the options market , but there isn’t a sufficiently developed inflation options market (at least in the US).  However, experience shows that market participants are unwilling to sell options with strikes either very low (say 0%) or very high (say 5%) at anywhere near theoretical prices, suggesting that the right distribution might be more fat tailed than a normal distribution.  This wouldn’t be shocking , since many financial variables have similar characteristics.
It also matters what measurement period you are working with. The inflation rate for a given 12month period in the future could have a wider distribution than the average inflation over a 20year period, which might be better behaved.
In the US , the center of the distribution can be estimated from the inflation bond and derivatives markets , and is in the area of 2% for long term forecasts, in line with the target of the Federal Reserve.