maths question

hi, please could i have help on question 13 of this paper? So i did the normal approximation, and then did inverse normal of 0.025, used the z value and worked out n to be 1239.209511 which rounds to 1239. But i'm confused by the last mark on the ms, why are they testing 1238 and 1239?
paper: https://www.ocr.org.uk/Images/621199-question-paper-pure-mathematics-and-statistics.pdf
ms: https://www.ocr.org.uk/Images/621390-mark-scheme-pure-mathematics-and-statistics.pdf
thanks!

The normal approximation is just that - an approximation. Hence the need to check the true binomial cumulative results for values close to the one indicated by the normal approximation.

but if i got 1239.209511, wouldn't i need to check between 1239 and 1240? thanks!

Checking one either side of the rounded Normal result would be sensible.

oh ok, so i worked out using binomial that p(x<=1238)= 0.023261 and p(x<=1239)=0.025112. The question says <0.025 so how is it 1239? Is it because the value is closer to 0.025? thank you!

The clue is in the wording of the question: P(X<n)<0.025, not P(X<=n)<0.025....