Normal distribution — Interpret 2.5%

Question

Why is the threshold placed at for a unnecessary-shutdown risk?

This practice question was inspired by Question 14(d) in the 2021 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: standardise to a z-score and use the matching standard-normal probability.Under a normal model, about of values lie within of , so each tail has about .
State the final answer clearly in the form the question requested.The upper of therefore begins near .

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

Verification: Course-level normal tail approximation with .

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