alleryStart learning →The total area under a normal probability curve must equal:
AExactly one
BExactly zero
COne hundred
DThe mean value
Answer & Solution
Correct answer: A. Exactly one
1. A probability distribution assigns total probability one to all outcomes.
2. The area under the curve must equal one.
3. That constraint is what links the height of the curve to its width.
4. A change in the standard deviation therefore changes the shape of the curve.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 6 'The Normal Distribution', sections 6.1-6.3_
Keep practising The Normal Distribution
Browse all The Normal Distribution questions for AP Statistics, or explore more Statistics topics.
Related questions
Complete the standardising ruleWhich band holds more data?True or false: the normal curveKey in the empirical ruleMatch each z-score to its shareRecognising the standard normal distribution matters because it can then be:The z-scores minus 2 and plus 2 correspond to which pair of original values in a distributIf about 68 percent of values lie within one standard deviation, the share lying outside t