If you're going to be pedantic, at least be overly so:
Assuming each of his figures is accurate to within half a percent: We need at least 67 people to be able to round to 1%, but we can't quite get 80% out of 67 or 68 people (we end up rounding to 79% or 81%.) It turns out 69 people is adequate -- 1/69 rounds to 1%, 55/69 rounds to 80%, and the remaining 13/69 also rounds to 19%.
Assuming each of his figures is accurate to within half a percent: We need at least 67 people to be able to round to 1%, but we can't quite get 80% out of 67 or 68 people (we end up rounding to 79% or 81%.) It turns out 69 people is adequate -- 1/69 rounds to 1%, 55/69 rounds to 80%, and the remaining 13/69 also rounds to 19%.