binomial <- rbinom(100000, 1000, .5)

$$\mu = \text{size} \cdot p$$ $$\sigma = \sqrt{\text{size} \cdot p \cdot (1 - p)}$$

expected_value <- 1000 * .5
variance <- 1000 * .5 * (1 - .5)
stdev <- sqrt(variance)

normal <- rnorm(100000, expected_value, stdev)