Large Counts Condition the np ≥ 10 check.
Large Counts is the condition you check before running inference for proportions. The rule: np ≥ 10 AND n(1−p) ≥ 10. Skip the check on the FRQ and you lose a point.
The condition
Before running inference for a proportion (z-test, z-interval), you must verify that the sampling distribution is approximately normal. The Large Counts Condition is the check: both np ≥ 10 and n(1−p) ≥ 10.
For a confidence interval, use p̂ (sample proportion) in place of p. For a hypothesis test, use p₀ (null-hypothesis proportion).
How to write it on the FRQ
The AP rubric explicitly awards 1 point for stating Large Counts. Write it in plain English with the numbers:
“n p̂ = 50 × 0.6 = 30 ≥ 10, and n(1−p̂) = 50 × 0.4 = 20 ≥ 10, so the Large Counts Condition is satisfied.”
Plug in actual values. Don’t just write “the condition is met.”
Frequently asked questions
Quick answers — written by humans, not a chatbot.
What if np or n(1−p) is less than 10?
You can’t use the normal approximation. AP usually steers you to a different test (e.g., exact binomial) or notes that inference isn’t appropriate.
Is Large Counts the same as the Normal Condition?
For proportions — yes. For means, the Normal Condition is different (use the sample distribution shape or CLT for n ≥ 30).