The area under the normal curve

Who contributed to the development of the normal curve?

• Abraham DeMoivre

• Marquis de Laplace

• Karl Friedrich Gauss

• Karl Pearson.

What other names has the normal curve been called?

The Laplace-Gaussian curve or the Gaussian curve.

What is the shape of the normal curve?

A bell-shaped, smooth, mathematically defined curve that is highest at the center and tapers off on both sides.

How far does the normal curve extend?

Theoretically, from negative infinity to positive infinity.

What does it mean when the normal curve approaches the X-axis asymptotically?

It gets closer and closer to the axis but never touches it.

Is the normal curve skewed?

No, it is perfectly symmetrical.

In a normal curve, how are the mean, median, and mode related?

They all have the same exact value.

What are the tails of the normal curve?

The extreme areas of the curve beyond ±2 to ±3 standard deviations from the mean

What do the tails of the normal curve represent in intelligence testing?

Individuals who are 2 or more standard deviations below the mean (IQ 70–75 or lower = intellectual disability) or above the mean (IQ 125–130 or higher = gifted).

Why are the tails of the normal curve significant in real life?

Scores in the tails indicate deviation from the norm, which can lead to major differences in education, parental expectations, social adjustment, and life opportunities.

What concept did Robinson et al. (2000) highlight about the tails of the normal curve?

That individuals at the tails share intellectual deviance and require different adjustments in life compared to average individuals.

How can knowledge of the area under the normal curve help in test score interpretation?

It shows where a score falls compared to others and indicates whether a person is exceptional, average, or below average in ability.

Example: What does it mean if a student scores nearly 3 SDs above the mean on a spelling test?

The student is exceptionally gifted (likely knows very advanced words such as asymptotic and leptokurtic).