Why School B's Normal Curve Is Right of School A's Due to Higher Mean

Conditions

• The horizontal axis represents scores and increases to the right.
• The score distributions of both schools are close to normal distributions.

Reasoning, step by step

1. Identify the mean score for School A, which is 60.
2. Identify the mean score for School B, which is 65.
3. Compare the two means: $65 > 60$.
4. Apply the property that the mean determines the horizontal position of the normal curve.
5. Conclude that School B's curve center is to the right of School A's curve center.

Example

The video states: 'School A has mean 60, below School B’s 65, so the thick curve’s center is left of the thin curve’s center.'

Common misconceptions

• Believing that the curves have disjoint supports; both normal densities still have support on the entire real line.
• Thinking that a higher mean implies a taller curve; the mean only controls horizontal position, not height.

Watch the explanation

Connected concepts

Explore next

• Why can't this problem rely only on the mean to select the graph?
• How does the standard deviation affect the shape of the normal curve?
• What is the geometric meaning of the area under the normal distribution curve?