Normal Distribution

The 68-95-99.7 rule states.

68% of the data lie within 1 standard deviation of the mean, 95% of the data will lie within 2 standard deviations of the mean, 99.7% of the data will lie within 3 standard deviations of the mean.

What is the Empirical Rule?

68-95-99.7

We call an observation unusual when?

An event is unusual if the absolute value of its z-score is greater than 2. z < -2 or if z > 2.

How is a normal density curve determined?

By the mean, and the standard deviation.

Calculate the z-score given the mean and SD

Subtract the mean and divide by the standard deviation.

Properties of a normal density curve

Symmetric and has a bell-shafted curve. Referred to as a normal distribution (Gaussian Distribution). 1. The total area under the curve equals 1. 2. The density curve always lies on or above the horizontal axis.

Where do you look to find the probability of a random value?

The area under the curve.

Probability applet allows us to use?

z-scores to calculate proportions, probabilities, and percentiles

Calculate probability as area under a normal density curve

Obtaining an observation less than (or equal to) that value under a normal curve that is to the left of z.

Assess normality using a QQ-plot

Graph that is used to assess if data are normally distributed. If points in the Q-Q plot are in a straight line, then we conclude that the data are normally distributed. Analyze/Descriptive Statistics/Explore Click on the variable you want to analyze. Click plots.

A z-score tells us?

How many standard deviations away from the mean a given value is. It is calculated as: z = value - mean = x - u standard deviation 0

What are the characteristics of a normal density curve?

Is symmetric and bell-shaped. The curve lies above the horizontal axis and the total area under the curve is equal to 1.

A Q-Q plot is used to

assess whether or not a set of data is normally distributed.

A standard normal distribution

has a mean of 0 and a standard deviation of 1.