Stats 4.3Concept7 parts

The Normal Distribution

Know the Gaussian's shape, the 68–95–99.7 rule, and z-scores.

In this lesson7 parts

  1. 01Choose a population before drawing a curve
  2. 02Build a normal model from height
  3. 03Read area and cumulative probability
  4. 04Standardize, then count actual heights
  5. 05Apply the same rule to ALT
  6. 06State the decision and its limits
  7. 07Reproduce and challenge

Key terms

The words this lesson introduces, each in one line. The module’s glossary collects them all.

ALT
Alanine aminotransferase, a laboratory measurement reported in U/L.
observed distribution
Counts or fractions of recorded values.
mean, μ
Arithmetic average used as the fitted curve's centre.
standard deviation, σ
Typical scale of deviations, in the measurement's units.
normal distribution
Symmetric distribution specified by mean and SD.
probability density function, PDF
Curve whose interval areas give probabilities.
cumulative distribution function, CDF
Probability at or below a threshold.
tail probability
Probability beyond a chosen boundary; 2.275% above z = 2.
z score
Distance from the mean measured in SD units.
standard normal
Normal model with mean zero and SD one.
normal approximation
Using a normal model where observed shape is close enough for a stated purpose.

Quiz 5 questions

Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.

Practice

Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.

The self-checking notebook for this lesson is The normal distribution and residual shape.

Common mistakes

What you will see when it goes wrong, why it happens, and the fix.

Where it’s used

Where this lesson’s ideas turn up in real work.