Variation 2 · answer guide

Binomial distribution — Compute threshold n

Question

For and bound , which inequality correctly finds ?

This practice question was inspired by Question 8 in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: identify the random variable and its parameters before using the matching probability formula.From get .
Finish the calculation, then check that the result meets the question’s conditions.Here and .
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Numeric: , so after strictness.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.