Binomial distribution — Mean and z-score steps

Question

For , , find and the -score for (use ), then approximate given .

This practice question was inspired by Question 12(c) 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.; .
State the final answer clearly in the form the question requested.Answer: approximately .

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

Verification: Matches the NESA sample numerical path.

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