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What is Normal Distribution in AQA Core Maths?

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danica

28/05/2023

Maths

AQA Paper 2A Core Maths Notes

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Normal distribution (a level only)

What is Normal Distribution in AQA Core Maths?

A comprehensive guide to Understanding normal distribution in AQA Core Maths, focusing on probability calculations and statistical analysis.

  • The guide covers essential topics in Core Mathematics including Normal Distribution, Correlation & Regression, and Confidence Intervals
  • Detailed explanations of standardization processes and probability calculations using normal distribution tables
  • In-depth coverage of correlation analysis, regression calculations, and confidence interval determinations
  • Practical examples and step-by-step procedures for solving mathematical problems
  • Essential formulas and notations for statistical analysis
...

28/05/2023

841

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 2: Normal Distribution Fundamentals

This section explains the fundamental characteristics of normal distribution and introduces standard normal distribution notation. The page details the symmetrical nature of the normal curve and its key properties.

Definition: Normal distribution is a continuous probability distribution that follows a bell-shaped curve.

Vocabulary: X~Nμ,σ2μ,σ² represents normal distribution notation where μ is the mean and σ² is the variance.

Highlight: The normal distribution curve is characterized by six standard deviations, with three on either side of the mean.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

View

Page 3: Standardization Process

This page covers the standardization process for converting normal distribution to standard normal distribution. It explains how to transform data values to standardized scores.

Example: The standardization formula Z = X−μX-μ/σ converts any normal distribution to standard normal distribution.

Definition: Standardization is the process of converting a normal distribution to have a mean of 0 and standard deviation of 1.

Highlight: The 68-95-99.7 rule shows that 68% of data falls within one standard deviation, 95% within two, and 99.7% within three.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

View

Page 4: Probability Calculations

This section details methods for Calculating probabilities using standard normal distribution tables. It covers both "less than" and "more than" probability calculations.

Example: To find PZ>0.7Z > 0.7, calculate 1 - PZ<0.7Z < 0.7 using the standard normal distribution table.

Highlight: Probability calculations utilize symmetry properties of the normal distribution.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

View

Page 5: Finding Values Using Standardization

This page explains how to find unknown values using the standardization formula and probability tables.

Definition: The standardization formula can be rearranged to find any missing value when given probability and other standard values.

Example: When probability is less than 0.5, use the inverse probability method to find Z-values.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

View

Page 6: Correlation and Regression Analysis

This section focuses on Interpreting correlation and regression in mathematical studies, explaining the relationship between variables and regression line calculations.

Definition: PMCC Pearson′sMomentCorrelationCoefficientPearson's Moment Correlation Coefficient measures correlation strength between -1 and +1.

Vocabulary: Extrapolation refers to predicting values outside the data range, which can be unreliable.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

View

Page 7: Confidence Intervals

This final page covers confidence interval calculations and their interpretation in statistical analysis.

Definition: Confidence intervals provide a range within which we believe the true population parameter lies.

Example: For an 80% confidence interval, use Z = 1.2816 from the standard normal table.

Highlight: Sample size affects the width of confidence intervals through the standard error calculation.

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Subjects

Maths

Mechanics

Statistical distributions

Normal distribution (a level only)

 

Maths

•

841

•

22 Jul 2025

•

7 pages

What is Normal Distribution in AQA Core Maths?

user profile picture

danica

@danica_n

A comprehensive guide to Understanding normal distribution in AQA Core Maths, focusing on probability calculations and statistical analysis.

  • The guide covers essential topics in Core Mathematics including Normal Distribution, Correlation & Regression, and Confidence Intervals
  • Detailed explanations of standardization... Show more

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 2: Normal Distribution Fundamentals

This section explains the fundamental characteristics of normal distribution and introduces standard normal distribution notation. The page details the symmetrical nature of the normal curve and its key properties.

Definition: Normal distribution is a continuous probability distribution that follows a bell-shaped curve.

Vocabulary: X~Nμ,σ2μ,σ² represents normal distribution notation where μ is the mean and σ² is the variance.

Highlight: The normal distribution curve is characterized by six standard deviations, with three on either side of the mean.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 3: Standardization Process

This page covers the standardization process for converting normal distribution to standard normal distribution. It explains how to transform data values to standardized scores.

Example: The standardization formula Z = X−μX-μ/σ converts any normal distribution to standard normal distribution.

Definition: Standardization is the process of converting a normal distribution to have a mean of 0 and standard deviation of 1.

Highlight: The 68-95-99.7 rule shows that 68% of data falls within one standard deviation, 95% within two, and 99.7% within three.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 4: Probability Calculations

This section details methods for Calculating probabilities using standard normal distribution tables. It covers both "less than" and "more than" probability calculations.

Example: To find PZ>0.7Z > 0.7, calculate 1 - PZ<0.7Z < 0.7 using the standard normal distribution table.

Highlight: Probability calculations utilize symmetry properties of the normal distribution.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 5: Finding Values Using Standardization

This page explains how to find unknown values using the standardization formula and probability tables.

Definition: The standardization formula can be rearranged to find any missing value when given probability and other standard values.

Example: When probability is less than 0.5, use the inverse probability method to find Z-values.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 6: Correlation and Regression Analysis

This section focuses on Interpreting correlation and regression in mathematical studies, explaining the relationship between variables and regression line calculations.

Definition: PMCC Pearson′sMomentCorrelationCoefficientPearson's Moment Correlation Coefficient measures correlation strength between -1 and +1.

Vocabulary: Extrapolation refers to predicting values outside the data range, which can be unreliable.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 7: Confidence Intervals

This final page covers confidence interval calculations and their interpretation in statistical analysis.

Definition: Confidence intervals provide a range within which we believe the true population parameter lies.

Example: For an 80% confidence interval, use Z = 1.2816 from the standard normal table.

Highlight: Sample size affects the width of confidence intervals through the standard error calculation.

Paper 2A Core Maths Notes AQA Realising potential #/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350) AQA Cert

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Page 1: Introduction to AQA Level 3 Mathematical Studies

This page introduces the AQA Certificate Level 3 Mathematical Studies 13501350 specification, outlining the key topics covered in Paper 2A. The course content focuses on Normal Distribution, Correlation & Regression, and Confidence Intervals.

Highlight: The specification is designed for teaching from September 2014 with first examinations from June 2016.

Definition: Level 3 Mathematical Studies is an advanced mathematics course that builds upon GCSE mathematics knowledge.

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user