  We calculate the dispersion measure (DM) contributed by the intergalactic
medium (IGM) to the total measured DM for fast radio bursts (FRBs). We use the
MareNostrum Instituto de Ciencias del Espacio (MICE) Onion Universe simulation
(Fosalba et al. 2008) to track the evolution of the dark matter particle
density over a large range of redshifts. We convert this dark matter particle
number density to the corresponding free electron density and then integrate it
to find the DM as a function of redshift. This approach yields an intergalactic
DM of $\rm DM_{\rm IGM}(z = 1) = 800^{+7000}_{-170}$ pc cm$^{-3}$, with the
large errors representative of the structure in the IGM. We place limits on the
redshifts of the current population of observed FRBs. We also use our results
to estimate the host galaxy contribution to the DM for the first repeater, FRB
121102, and show that the most probable host galaxy DM contribution, $\rm
DM_{\rm host} \approx 310$ pc cm$^{-3}$, is consistent with the estimate made
using the Balmer emission lines in the spectrum of the host galaxy, $\rm
DM_{\rm Balmer} = 324$ pc cm$^{-3}$ (Tendulkar et al. 2017). We also compare
our predictions for the host galaxy contribution to the DM for the observations
of FRB 180924 (Bannister et al. 2019) and FRB 190523 (Ravi et al. 2019), both
of which have been localized to a host galaxy.
