Cumulative totals never decrease, so the problem doesn't actually make sense as stated. What is intended is that you pretend that each of 169605 cases from March 17th independently has a 0.6 probability of giving rise to a case on June 17. Again, that's not close to how a virus spreads, and "reduce by 60%" should mean the probability is 0.4, but we will ignore these.
You can use a normal approximation to approximate the probability, and I recommend that. If X~Binomial(N=169605,p=0.6), then E[X] = np and Var[X] = np(1-p). You can approximate X by a normal distribution with the same mean and variance. A normal approximation is reasonably accurate when np and n(1-p) are both at least 10 which is easily the case here.
If you want a simulation instead, you will want to draw from this distribution many times. You can do this using R. The function rbinom() produces trials from a binomial distribution relatively efficiently, e.g., rbinom(100,169605,0.6) gives a vector with 100 trials. You can also do this in Excel. =BINOM.INV(169605,0.6,RAND()) gives a single trial, and you can copy this into a large array.
