Calculating Probabilities Under a Normal Curve

These flashcards cover key vocabulary relating to calculating probabilities under a normal curve, including definitions and explanations crucial for understanding normal distributions.

Normal Curve

A graphical representation of a normal distribution, showing the probability of occurrences of values.

Cumulative Area

The area under the normal curve from negative infinity to a specific z value, representing the cumulative probability up to that point.

Standard Normal Distribution

A normal distribution with a mean of 0 and a standard deviation of 1.

z-Score

A statistical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations.

Probability Table (Table z)

A table that provides the cumulative area under the standard normal curve for different z-scores.

Standard Deviation

A measure that quantifies the amount of variation or dispersion of a set of data values.

Mean (µ)

The average or central value of a set of data, representing the center of the distribution.

Finding Area

The process of calculating the probability for a certain range of values in a normal distribution.

Standardize

To convert a raw score (y) into a z-score to allow for comparisons across different scales and distributions.

P(z < a*)

The probability that a standard normal variable z is less than a given value a*.

P(a* < z < b*)

The probability that the standard normal variable z is between two values a* and b*.

Theorem of Normal Distribution

If a variable y is normally distributed with mean µ and standard deviation s, then the standardized variable z is also normally distributed as z ~ N(0, 1).