What does “inside standard deviation from 500” mean?
Having a small p-value is exactly the same thing, at least for approximately normally distributed things like this, as being multiple standard deviations away from the norm.
The specific number here is neither “like p=0.01” nor within 1σ of the mean. Variance of a binomial distribution is npq=250, so standard deviation is just under 16. Being at least 20 away from 500 is approximately a p=0.2 event.
What does “inside standard deviation from 500” mean?
Having a small p-value is exactly the same thing, at least for approximately normally distributed things like this, as being multiple standard deviations away from the norm.
The specific number here is neither “like p=0.01” nor within 1σ of the mean. Variance of a binomial distribution is npq=250, so standard deviation is just under 16. Being at least 20 away from 500 is approximately a p=0.2 event.