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Statistical Analysis

HSC HSC Mathematics Advanced · 2024 content registry · first HSC 2027

Official NSW Curriculum syllabus and implementation timeline ↗Download questions and solutions PDF
S1.1S2.1S3.1
Assessment evidence

What these examples cover

These examples show assessable skills, not an official HSC topic weighting or prediction. The 2024 NSW syllabuses have their first HSC examination in 2027; students sitting the 2026 HSC continue under the applicable 2017 syllabus.

Teacher check

Teacher verification note: check the mathematics, notation, permitted technology and syllabus fit for your cohort before classroom or assessment use.

3 deterministic examples

Statistical Analysis questions with worked solutions

Each question is generated from an existing curriq QDSL archetype at a fixed seed. Marks and catalog content mappings travel with the generated question.

Worked example 1

2 marksadv-s3-1
Recover a normal mean A normally distributed set has score 10 at z=−2z=-2 and score 22 at z=1z=1. Calculate the mean.
Part a · 2 marks

Find the mean of the scores.

Worked solution

Answer: 18

  1. Z Score Difference: 4
  2. Z Score Formula: 18

Catalog reference: adv_cssa20_normal_mean_from_z_scores · seed 41001

Worked example 2

2 marksadv-s1-3
A number observed in a conditioned dice sum Two ordinary dice are rolled and their sum is 7. Find the probability that 5 appeared at least once.
Part a · 2 marks

Find the conditional probability.

Worked solution

Answer: 1/3

  1. Conditional Sample Space: 6
  2. Count Favourable Outcomes: 2

Catalog reference: adv_cssa20_conditional_dice_observed_number · seed 41001

Worked example 3

1 markadv-s1-1
Drawing coloured balls A bag contains 5 red and 8 black balls. Two are drawn without replacement. Find the probability that the first is red.
Part a · 1 mark

Find the probability.

Worked solution

Answer: 5/13

  1. Single Draw Probability: 5/135/13.

Catalog reference: adv_pem23_q12a_first_red_probability · seed 41001

Content mapping and common errors

Statistical Analysis content identifiers

S1.1

Probability and Discrete Probability Distributions

Understand and apply probability; work with discrete random variables and their expected values.

Common student mistakes
  • ·Confusing P(A ∪ B) and P(A ∩ B) in the addition formula
  • ·Forgetting to check that probabilities sum to 1 in a distribution table
S2.1

The Binomial Distribution

Identify and apply the binomial distribution; calculate probabilities and expected values.

Common student mistakes
  • ·Not verifying the four conditions for a binomial distribution
  • ·Using the wrong value of p (complementary event errors)
S3.1

Normal Distribution

Apply the properties of the normal distribution; use z-scores; model data with normal distributions.

Common student mistakes
  • ·Incorrect z-score formula — dividing by σ² instead of σ
  • ·Forgetting to account for both tails of a symmetric probability

Source and methodology

Examples are deterministic curriq catalog generations from existing QDSL archetypes at the published fixed seed. The generator copies only student-facing prompts, mark allocations, topic mappings, display tables or options, checked answers and marking-path results into this resource.

Review the official NSW Curriculum source ↗

Other Advanced topics

Functions
3 content identifiers
Trigonometric Functions
3 content identifiers
Calculus
6 content identifiers
Exponential and Logarithmic Functions
2 content identifiers
Financial Mathematics
1 content identifier

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