Variation 3 · answer guide
Binomial distribution — p=0.25, n=1200
Question
A population has proportion . A random sample of size is taken and is the sample proportion.
(i) Show that .
(ii) Hence approximate using the standard normal table, correct to two decimal places.
This practice question was inspired by Question 11(f) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Step by step
- Set up the solution: identify the random variable and its parameters before using the matching probability formula.(i) .
- Simplify the previous line carefully, keeping exact values where possible.(ii) .
- Finish the calculation, then check that the result meets the question’s conditions..
- State the final answer clearly in the form the question requested.Table: .
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: Nice exact makes the -score exact; both parts required.
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2023 HSC Extension 1 paper Question 11(f)