The Normal Distribution

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Next Section: A2 Statistics General Support

Word Doc

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A2 Maths – Statistics – Normal Distribution

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Normal Distribution 1 • Intro and Definitions • Stats2 Ex3A • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 1-11✦

Extra Questions

• Dr Frost Questions (Very short)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 640a: Know the conditions for the normal distribution to be a suitable model. (not yet active)
• 640b: Understand the notation X sim mathcalN(mu, sigma²) and use this to sketch normal curves. (not yet active)
• 640c: Calculate the number of standard deviations a value has from the mean. (not yet active)
• 640d: Use the 68-95-99.7 rule to find the probability of values within a given number of standard deviations of the mean, in context. (not yet active)
• 640e: Use the 68-95-99.7 rule to find the probability of more general ranges, in context. (not yet active)
• 640: Exam Practice: Properties of the normal distribution and finding the probability of ranges

Other Videos

The Normal Distribution with a calculator

Courtesy of Maths Genie (Up to 2:15)

Enrichment Video

Why π is in the normal distribution (beyond integral tricks)

3Blue1Brown: Why π is in the normal distribution (beyond integral tricks)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2 Maths – Statistics – Calculating Probabilities on Normal Distribution

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Normal Distribution 2 • Finding Probabilities using your Calculator • Stats2 Ex3B • 🎲

Normal Distribution 3 • Worded example combined with binomial • Stats2 Ex3B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 12-15✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 640f: Calculate probabilities with the normal distribution (no context).
• 640g: Calculate probabilities with the normal distribution in context. (not yet active)
• 642a: Determine a conditional probability of a range using a normal distribution. (not yet active)
• 642c: Use the symmetry of a normal distribution to find conditional probabilities. (not yet active)
• 642e: Solve more difficult problems involving conditional probabilities for a normal distribution. (not yet active)
• 640: Exam Practice: Properties of the normal distribution and finding the probability of ranges
• 642: Exam Practice: Conditional probabilities involving a normal distribution

Further Practice

• Practise Questions

Other Videos

The Normal Distribution with a calculator

Courtesy of Maths Genie (From 2:15 up to 8:50)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2 Maths – Statistics – Inverse Normal Distribution

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Normal Distribution 4 • Inverse using your Calculator • Stats2 Ex3C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 16-19✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 641a: Use the inverse normal distribution (no context).
• 641b: Use the inverse normal distribution in context. (not yet active)
• 641c: Determine a quartile of a normal distribution. (not yet active)
• 641d: Use the inverse normal distribution with a double inequality.
• 641e: Use the inverse normal distribution with a double inequality, where the variable is used twice. (not yet active)
• 642b: Determine the median of a restricted range within a normal distribution. (not yet active)
• 642d: Determine a value at a more general position given a restricted range in a normal distribution. (not yet active)
• 641: Exam Practice: Inverse normal distribution
• 642: Exam Practice: Conditional probabilities involving a normal distribution

Further Practice

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2 Maths – Statistics – Standard Normal Distribution

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3D Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Normal Distribution 5 • Standard, z-values • Stats2 Ex3D • 🎲

Normal Distribution 6 • z-values practice • Stats2 Ex3D • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 20-25✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 643a: Understand the Z distribution and convert values to a z-value. (not yet active)
• 643: Exam Practice: Standard normal distribution (including unknown mean and standard deviation)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• WW Multiple Choice Quiz (PowerPoint)
• Math = Love (Sarah Carter)
  • Introducing Z-Scores Notes

A2 Maths – Statistics – Finding mean and standard deviation with normal distribution

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3E Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Normal Distribution 7 • Missing Mean and/or Standard Deviation • Stats2 Ex3E • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 26-29✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 643b: Determine the mean of a normal distribution (no context).
• 643c: Determine the standard deviation of a normal distribution (no context).
• 643d: Determine the mean and standard deviation of a normal distribution (no context).
• 643e: Determine the mean or standard deviation of a normal distribution in context. (not yet active)
• 643f: Determine the mean or standard deviation of a normal distribution where the probability of a two-ended range is given in context. (not yet active)
• 643g: Determine the mean and standard deviation of a normal distribution in context. (not yet active)
• 643: Exam Practice: Standard normal distribution (including unknown mean and standard deviation)

Further Practice

• Practise Questions

Other Videos

The Normal Distribution with a calculator

Courtesy of Maths Genie (From 8:50)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheet

A2 Maths – Statistics – Approximating the Binomial with the Normal Distribution

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. Up to 6:57

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3F Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Normal Distribution 8 • Approximating a Binomial, Continuity Corrections • Stats2 Ex3F • 🎲

Normal Distribution 9 • Full Binomial Approximation example • Stats2 Ex3F • 🎲

Normal Distribution 10 • Mix of Binomial and Normal exam question • Stats2 Ex3F • 🎲

Normal Distribution 11 • Extra Binomial Approximation example • Stats2 Ex3F • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (up to 10:24)

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 30-37✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 644a: Approximate a binomial distribution using a normal distribution. (not yet active)
• 644b: Use a continuity correction to give an equivalent continuous range to a discrete one. (not yet active)
• 644c: Determine the probability of a range by using a normal approximation to a binomial distribution (no context).
• 644d: Determine the probability of a range by using a normal approximation to a binomial distribution in context. (not yet active)
• 644e: Use a normal approximation to a binomial distribution to determine the k in P(X ≤ k) (not yet active)
• 644f: Use a normal approximation to a binomial distribution to determine the number of trials n. (not yet active)
• 644: Exam Practice: Normal distribution as an approximation to a binomial distribution

Further Practice

• Practise Questions

Other Videos

Using the Normal Distribution to approximate the Binomial Distribution

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• MadAsMaths (T. Madas)
  • Distributional Approximations Binomial to Normal Q1–12 (difficulty 2–5 of 5)

Activities & Resources

• Ben Sparkes Geogebra Binomial Distribution Explorer & Binomial Distribution
• rhalai6.310 Kahoot for Continuity Corrections
• mcmaster.ca Continuity Corrections Article (Some nice diagrams)
• SRWhitehouse
  • Normal approximations✦

A2 Maths – Statistics – Hypothesis Testing with the Normal Distribution

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3G Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Normal Distribution 12 • Hypothesis Testing on the Sample Mean • Stats2 Ex3G • 🎲

Normal Distribution 13 • Hypothesis Testing Critical Regions • Stats2 Ex3G • 🎲

Normal Distribution 14 • Mixed skill exam question • Stats2 Ex3 ExamQ • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 38-46✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 644g: Use a normal approximation to conduct a hypothesis test on a proportion p. (not yet active)
• 645a: Determine the distribution for the sample mean barX (not yet active)
• 645b: Conduct a one-tailed hypothesis test on the mean of a population. (not yet active)
• 645c: Conduct a two-tailed hypothesis test on the mean of a population. (not yet active)
• 645d: Determine the critical region for the sample mean. (not yet active)
• 850b: Use the Central Limit Theorem to calculate a probability involving a sample mean, where the population distribution is normal.
• 644: Exam Practice: Normal distribution as an approximation to a binomial distribution
• 645: Exam Practice: Hypothesis tests on the mean of a population by using a sample
• 850: Exam Practice: Central Limit Theorem for sample mean

Further Practice

• Practise Questions

Other Videos

Mean of Normal Distribution Hypothesis Testing

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Mathshelper (Jon Stone)
  • Continuous Hypothesis Testing
  • Discrete Hypothesis Testing With Approximation
• Physics & Maths Tutor
  • Hypothesis testing: Tests on Normal: Questions 2021–24 · Mark scheme · Model answers
• MadAsMaths (T. Madas)
  • Normal Distribution: Sampling, Confidence Intervals & Hypothesis Tests Hypothesis Testing Q1–9, 11–20, 22; Critical Regions Q1–3 (difficulty 2–4 of 5)

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Jethwa Maths Starter Activities
• Mathsaurus Normal Distributions & Hypothesis Testing (Video Solutions Pending)
• PMT
  • Edexcel Normal distribution
  • Edexcel Hypothesis tests – Tests on Normal
  • AQA Normal Distribution
  • AQA Hypothesis Testing
  • OCR The Normal Distribution
  • OCR Hypothesis Testing for The Normal Distribution
  • OCR MEI Normal Distribution
  • OCR MEI Hypothesis Testing for Normal Mean
  • Cheat Sheet
• Transum
  • Exam-style questions: Normal Distribution

Other Whole Topic Resources

• Acute Learning Conditional Normal Problem Pairs as PowerPoint or PDF
• Lucyjc1612 Summary Poster (Normal Distribution)

Worksheets

• Mathshelper (Jon Stone)
  • Normal Distribution
• MathedUp
  • Normal Distribution: Questions · Challenge · Answers
• Maths Genie
  • The Normal Distribution: Questions · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Statistical distributions (exam questions)
• Physics & Maths Tutor
  • Normal Distribution: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• SRWhitehouse
  • Normal Distribution Question Sheets✦
  • Normal Distribution Matching Activity✦
• Dr Oliver Mathematics
  • Normal Distribution Questions✦ (answers✦)
• MadAsMaths (T. Madas)
  • Normal Distribution Calculations Various Q1–7, 9, 11, 12, 14–24 (difficulty 2–4 of 5)

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Probability distributions✦
  • Probabilities and Normal curves (more challenging)✦
• variationtheory.com
  • Normal distribution: fill in the gaps✦
• Andy Lutwyche
  • Erica’s Errors