Statistical Sciences 2244A/B Lecture Notes - Lecture 6: Binomial Distribution, Dont, Standard Deviation
22 May 2018
School
Department
Professor
Stats 2244
Continuous RV & Normal Distributions
Density curves, N(μ,σ, QQ plots, z distributions
- Binomial distributions and normal distributions are probability models used in this course
The Normal Distribution, N(μ,σ
- DONT (AVE TO KNOW T()S FORMULA - its just to show that normal is
defined by that function – you cant just look at a histogram and decide that
its normal
- If we are dealing with a normal distribution, the probability of x approaches
0
- Normal distributions are continuous distributions
o So if we model the normal distribution in a density curve, then the
area would be 0 bc there is no width part if you chose one point on
the normal distribution
o So we can never calculate the probability of a particular value
o So we look at a definable area under the curve - look for probabilities like P(X<x)
- Every normal distribution has the same distribution of the area under the curve
o +/- 2 SDs is about 95% of the distribution under the curve
o +/- 3 SDs is about 99.7% of the distribution under the curve
Assessing Normality
- QQ plot lets us assess if a particular distribution is a normal distribution
- Top left image
o Not normal
o The tails are way off the line
- bottom left graphs:
o not normal
o the tails are creating a non-random deviation from the predicted line – causing it to be
non-normal
- Right graph: looks reasonably normal
o Even though there is some deviation from the top and bottom, its not nearly as deviated
as the other 2 graphs on the left
- What happens if our data are not normal?
o In this course, we are assuming that the data is normal
o So usually we would do a transformation but in this course were not going to learn how
to do that
o SO ON AN EXAM )F T(E DATA )S NOT NORMAL, C(OOSE NOT ENOUGH INFORMATION
TO ANSWER T(E QUEST)ON
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