Zadanie 8f, Paper 2, maj 2025, TZ3, Matematyka AA IB SL
Wzorowane na: Matematyka AA IB SL — maj 2025, TZ3, Paper 2 (zadania wzorowane), pytanie 8(f). Treść, dane i kontekst są zmienione; sprawdzane umiejętności, format i punktacja jak w oryginale.
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Zadanie
Wspólne informacje do wiązki zadań
A maker festival offers soldering and 3D-printing sessions. Different visitors make their participation decisions independently. A visitor joins soldering with probability 0.42. There are 1200 visitors on Saturday. Let D count those who join soldering.
Polecenie
On Sunday there are n visitors, and each joins 3D printing with probability 0.68. The probability that at most 450 join is approximately 0.762. Find n.
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Use and search integer n. At n=649,650,651 the values are 0.7794734343…,0.7618304021…,0.7434816485… . Thus n = 650. A continuity-corrected normal equation gives n≈650.04 and the same integer. Without a continuity correction, the normal equation (450−0.68n)/sqrt(0.68·0.32n)=Φ⁻¹(0.762) gives n≈649.3057159; accept n=649 when this approximation is shown.
Schemat punktowania
M1: a table, integer search or inverse-binomial approach, evidenced by at least one correct CDF value at an n. Also allow a valid normal-model setup with the appropriate quantile for 0.762. A2: n=650. Also award the two answer marks for n=649 only when supported by a demonstrated normal approximation without continuity correction. The exact binomial answer remains n=650.
Komentarz. Paper 2: a graphic display calculator and AA SL formula booklet are available. Give exact values or three significant figures unless specified otherwise. Show the relevant equations or calculator inputs. Equivalent valid methods are accepted.