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probability distributions & comparisons

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: probability distributions & comparisons

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about probability distributions & comparisons. Then check against the key terms: key terms from probability distributions & comparisons. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: key terms from probability distributions & comparisons.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: probability distributions & comparisons. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Statistics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look

Start with the revision notes summary, then attempt: explain the key ideas of probability distributions & comparisons

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about probability distributions & comparisons.

Lesson 2: Core Concepts: probability distributions & comparisons

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on probability distributions & comparisons. Check them against the notes below.

Main Content (35 minutes)

Key Fact: A probability distribution lists all possible outcomes with their associated probabilities; the total probability always sums to 1
Key Fact: Binomial distribution models the number of successes in n independent trials, each with the same probability p of success; P(X = r) = ²ⁿCᵣ × pʳ × (1−p)ⁿʻʳ where X~B(n, p)
Key Fact: For a binomial distribution: mean = np and variance = np(1−p); these are the expected value and spread
Key Fact: The normal distribution is a continuous bell-shaped curve, fully defined by its mean (μ) and standard deviation (σ); notation X~N(μ, σ²)
Key Fact: The 68–95–99.7 rule: approximately 68% of data lies within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ
Key Fact: The normal distribution is symmetric about the mean; the mean, median and mode are all equal

Practice (10 minutes)

Q: explain the key ideas of probability distributions & comparisons

Answer:

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: probability distributions & comparisons

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: key terms from probability distributions & comparisons. Define each in one sentence.

Main Content (35 minutes)

Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.

Work through the practice questions on the revision notes page for this topic.

Plenary (5 minutes)

Error Review

Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.

Lesson 4: Exam Practice: probability distributions & comparisons

Duration: 50 minutes

Starter Activity (5 minutes)

Command Words

Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).

Main Content (35 minutes)

Extended Answer

Extended question: Full-Mark Response The masses of apples from Farm A are normally distributed with mean 150 g and standard deviation 12 g. The masses of apples from Farm B are normally distributed with mean 160 g and standard deviation 20 g. An apple from Farm A has mass 174 g and an apple from Farm B has mass 180 g. Which apple is relatively heavier? Show your working. <div class="

Standardise each apple’s mass using z = (value − mean) ÷ SD. Farm A: z = (174 − 150) ÷ 12 = 24 ÷ 12 = 2.0 Farm B: z = (180 − 160) ÷ 20 = 20 ÷ 20 = 1.0 The Farm A apple is 2.0 standard deviations above its mean, while the Farm B apple is only 1.0 standard deviation above its mean. Therefore the Farm A apple is relatively heavier compared to its distribution.

Exam Tips: Always state the distribution notation: X~B(n, p) for binomial and X~N(μ, σ²) for normal | When using the 68–95–99.7 rule, first identify how many standard deviations from the mean the boundary values are | In comparison questions, compare both location (mean/median) and spread (SD/IQR), and always refer back to the context | For z-score questions, show the calculation clearly: z = (x − μ)/σ, then interpret the sign and magnitude | Check whether a question is asking for a binomial or normal approach by looking for keywords: ‘number of successes’ suggests binomial; ‘normally distributed’ suggests normal
Common Errors: ✗ Using σ² instead of σ when applying the 68–95–99.7 rule ✓ The rule uses standard deviation σ, not variance σ²; mean ± 2σ covers 95% ✗ Confusing discrete and continuous distributions ✓ Binomial is discrete (count successes); normal is continuous (measure values on a scale) ✗ Comparing raw scores across different distributions without standardising ✓ Convert to z-scores first to make fair comparisons on a common scale ✗ Assuming all data is normally distributed without checking ✓ Only use the normal distribution when told the data is normally distributed or when the distribution is symmetric and bell-shaped
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how probability distributions &amp; comparisons connects to another Statistics topic you have studied
  • Real-world: research one real-world use or example of probability distributions &amp; comparisons
  • Critical: "What are the limitations of the models used in probability distributions &amp; comparisons?"

Plenary (5 minutes)

Assessment Criteria
  • Got it: Confident explanation + correct worked examples
  • Getting there: Main points OK, needs support with detail
  • Not yet: Confused on key concepts - re-run Lesson 2

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)