Selecting the Correct Normal Curve Graph Based on Mean and Standard Deviation

Conditions

• The thick line represents School A and the thin line represents School B.
• School A has mean 60 and standard deviation 10.
• School B has mean 65 and standard deviation 5.

Reasoning, step by step

1. Compare the means: $60 < 65$, so School A's curve must be to the left of School B's curve.
2. Compare the standard deviations: $10 > 5$, so School A's curve must be wider and shorter than School B's curve.
3. Evaluate the options based on these two criteria.
4. Notice that option (B) has curves of equal height, which contradicts the different standard deviations.
5. Confirm that option (A) shows the thick line (School A) wider and shorter on the left, and the thin line (School B) narrower and taller on the right.
6. Select option (A) as the correct answer.

Example

The video states: 'Combine the checks: School A’s 60 and 10 match the broad, low thick curve on the left; School B’s 65 and 5 the narrow, high thin curve on the right. Diagram A fits.'

Common misconceptions

• Choosing an option based solely on the horizontal position without checking the curve shapes.
• Assuming that the peak heights can be equal for different standard deviations.

Watch the explanation

Connected concepts

Explore next

• Why can't the peak heights be the same when comparing two normal distributions with different standard deviations?
• What is the mathematical formula for the peak height of a normal distribution?
• How does the area under the normal distribution curve relate to its shape?