Variation 1 · answer guide

Binomial distribution — SD bound with p=1/2

Question

If , the smallest integer with is

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., so .
Finish the calculation, then check that the result meets the question’s conditions.At the SD equals , which is not strictly less; the smallest integer is .
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: Strict inequality forces rounding up past the equality case.

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