Normal Distribution
The bell curve describes many natural measurements.
About this topic
The normal distribution is the symmetric, bell-shaped curve centred at the mean, with spread set by the standard deviation. The empirical rule says about 68% of values lie within one SD of the mean, 95% within two and 99.7% within three.
A z-score, z = (x − μ)/σ, tells how many standard deviations a value lies above or below the mean, letting different data sets be compared on one scale. The total area under the curve is 1, so area represents probability, and the mean, median and mode coincide at the centre. Tables or calculators convert z-scores into percentages.
Example: if exam scores have mean 70 and SD 10, a score of 90 has z = 2, placing it above about 97.5% of students. Adult heights, measurement errors and many natural traits are approximately normal, because they result from many small independent effects, an idea captured by the central limit theorem.
The normal curve is used in quality control, standardised testing and science. Tips: not all data are normal, such as incomes, which are skewed; always check the shape first. A z-score beyond 2 or 3 in size flags an unusual value.
Key ideas
- Symmetric about the mean
- 68-95-99.7 rule
- Standard deviation sets the width
Quick check
Use cases: where Normal Distribution helps
- Homework: review the key idea behind Normal Distribution before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Normal Distribution without notes.
- Visual learning: play with the interactive lab to see how Normal Distribution changes when you adjust its inputs.
- Teaching a friend: explain Normal Distribution in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Normal Distribution?
The bell curve describes many natural measurements.
What will I learn in Normal Distribution?
Symmetric about the mean. 68-95-99.7 rule. Standard deviation sets the width.
Is Normal Distribution part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Normal Distribution lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Normal Distribution?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.