Net Promoter Score with a Margin of Error

NPS asks "how likely are you to recommend us?" on 0–10. Promoters answer 9–10, detractors 0–6. NPS = %promoters − %detractors (from −100 to 100).

Implement nps(scores) returning (nps, margin) where margin is the 95% margin of error: $1.96 \times 100 \times \sqrt{\frac{p + d - (p - d)^2}{n}}$ with proportions $p$ and $d$.