1. Chapter 7: Continuous Distribution
Spring 2016

2. Random Variable Random Variable Characteristics Example
Discrete Random Variable
Finite number of outcomes
Binomial Distribution
Continuous Random Variable
Unlimited number of possible outcomes
Uniform Distribution;
Normal,
Standard normal, Student’s t distribution
---What about P(x=X) in each case?

3. Continuous Distribution
Parameters
Mean
Spread
Condition
Normal
N(µ , σ ) σ
Use when σ is known
Standard Normal
N(0, 1) 1
Use when σ is known, after standardization
𝑧= 𝑥−𝜇 𝜎
Student’s t
t(df) df
Use when σ is unknown but s is known; standardizing by
𝑡= 𝑥−𝜇 𝑠

4. Finding Probabilities
Distribution
Probability
P(x<X)
Normal
Area under curve
NORM.DIST(X, µ , σ ,1)
Standard Normal
NORM.S.DIST(Z,1)
Student’s t
T.DIST(T,df,1)

5. Finding Probabilities
How about P(X>b)?
P(X>b)=1-P(X<b)
And P(a<X<b)?
P(a<X<b)=P(X<b)-P(X<a)

6. Finding values given probabilities
Distribution
Value at which P(x<X)=π
From standardized scores
Normal
X = NORM.INV(π, µ , σ) NA
Standard Normal
Z = NORM.S.INV(π)
𝑋=𝑍∗𝜎+𝜇
Student’s t
𝑇 = T.INV(π,df)
𝑋=𝑇∗𝑠+𝜇