Inheritance percentiles
Setting up the binomial distribution:
For generation F1 each parent (F0) has a 50% chance of contribution the chromosome (under your simplified model), i.e. p=0.5, n=46 for the binomial distribution. I assume that when you say the 'normal' range you are looking for the mean +- 1 standard deviation? For p=0.5, n=46: mean=23 with standard deviation=3.39116 which helps define: Pr(20≤X≤26)=0.698. So in about 70% of cases a child will inherit 20-26 of their chromosomes from one parent.
For generation F2 each grandparent has a 25% probability of contributing a chromosome so we use p=0.25, n=46 which gives: mean = 11.5, standard deviation=2.93684 Pr(9≤X≤14)=0.6936. So in about 70% of cases a grandparent will have contributed 9-14 chromosomes.