Understanding Normal Distribution and Z-Scores

These flashcards cover the key concepts related to Normal Distribution and Z-scores, highlighting definitions, properties, and interpretations essential for understanding statistical analysis.

Normal Distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Z-scores

A standardized score that indicates how many standard deviations a score is from the mean of the distribution.

Bell shape

The shape of a normal distribution curve, where most of the area falls in the middle.

Bilateral symmetry

A property of the normal distribution where the left side is a mirror image of the right side.

Standard Deviation (SD)

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

Proportion within one standard deviation

Roughly 68% of scores fall within one standard deviation of the mean in a normal distribution.

Proportion greater than two standard deviations

About 5% of scores fall more than two standard deviations from the mean.

Z Distribution

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

Magnitude of z-scores

Indicates how far a score is from the mean in units of standard deviations.

Direction of z-scores

Indicates whether a score is above (+) or below (-) the mean.

Probability within two standard deviations

The probability that a random sample mean will fall within two standard deviations of the mean is approximately 95%.

Z-table

A table that shows the proportion of values below a given z-score in a standard normal distribution.

Raw scores

The original scores collected from observations before being transformed into z-scores.

Percentile

The value below which a percentage of observations in a group of observations fall.

Area under the curve

The total probability represented by the distribution, which equals 1.00 or 100%.

Shaded region under the curve

The area of interest in a normal distribution, used to find proportions for specific z-scores.