What characterizes a normal distribution?
1. Mean 2. Standard deviation
Approximately how many standard deviations are on either side of the mean?
The _____ is the point of symmetry in a normal distribution.
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 ____.
Normal curves describe:
What determines the SPREAD of a Normal distribution?
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?
Which is left-skewed? Which is right-skewed?
What rule do all normal distributions follow?
In a normal distribution, approximately ___% of observations fall within σ of the µ.
In a normal distribution, approximately ___% of observations fall within 2σ of the µ.
In a normal distribution, approximately ___% of observations fall within 3σ of the µ.
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).