Home › AP Statistics › Statistics › The Normal Distribution › The total area under a normal probability curve …
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_
Related questions
Recognising 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 tA z-score of zero corresponds to a value that is:Two normal curves with different standard deviations must still have equal:A normal distribution is often described by the shape of its curve as:The z-scores that bound the middle 99.7 percent of a normal distribution are:Between one standard deviation and two, the extra share of values captured is about: