COB 191 Chapter 6

Continuous Random Variable

A variable that can take any value on a continuum

Normal Distribution

A symmetric

Mean = Median = Mode

All equal in a normal distribution

Range of Normal Distribution

−∞ to +∞

Probability in Normal Distribution

Measured as area under the curve

Total Area Under Curve

Equals 1

Probability of Exact Value

Always 0 for continuous distributions

Standard Normal Distribution

A normal distribution with mean 0 and standard deviation 1

Z-Score

Standardized value showing how far a data point is from the mean

Z-Score Formula

Z = (X − μ) / σ

Empirical Rule

68% within 1 SD

Standard Normal Table

Gives probability from −∞ to a given Z value

NORM.S.DIST

Excel function to find area (probability) for a Z-score

NORM.S.INV

Excel function to find Z-score from probability

P(X < a)

Area to the left of a

P(X > a)

Area to the right of a

P(a < X < b)

Area between two values

Symmetry of Normal Curve

Half the area lies on each side of the mean

Why Use Z-Scores

To standardize different normal distributions for comparison