What characterizes a normal distribution?

1. Mean 2. Standard deviation

Approximately how many standard deviations are on either side of the mean?

3

The _____ is the point of symmetry in a normal distribution.

Mean

The standard deviation in a normal distribution is the distance between _____ and _____.

Mean, and the point of inflection

Importance of normal distributions (2). 1. 2.

1. Describes many distributions of real data and "chance" outcomes 2. Models many roughly symmetric distributions for statistical inference

What do density curves describe?

Continuous probability distributions

Normal distributions are a type of ____.

Density curve

Normal curves describe:

Normal distributions

What determines the SPREAD of a Normal distribution?

Standard deviation

How will a normal curve looks with a smaller SD compared to a larger SD?

Smaller SD: taller Larger SD: shorter

Typically, do the mean and standard deviation describe the shape of most distributions?

No. Only in a Normal distribution.

How can we tell if a distribution is Normal?

By using a Normal Quartile Plot

Does this Q-Q plot display a normal distribution?

No. Right-skewed.

Which is left-skewed? Which is right-skewed?

What rule do all normal distributions follow?

68-95-99.7 rule

In a normal distribution, approximately ___% of observations fall within σ of the µ.

68%

In a normal distribution, approximately ___% of observations fall within 2σ of the µ.

95%

In a normal distribution, approximately ___% of observations fall within 3σ of the µ.

99.7%

Formula for z, when standardizing a distribution that has a mean µ, and SD, the standardized value of x is:

z = x - µ / σ

What does a z-score tell you?

How many standard deviations the original observation falls away from the mean, and in which direction (+ = how many standard deviations greater than the mean, - = how many standard deviations less than the mean).