Lecture_11,_Chap_7,__Sec_3

# Lecture_11,_Chap_7,__Sec_3 - Chapter 7 Section 3...

This preview shows pages 1–10. Sign up to view the full content.

Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 6 Section 2 – Slide 1 of 25 Chapter 7 Section 3 Applications of the Normal Distribution

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Applications of the Normal Distribution Learning objectives Find and interpret the area under a normal curve Find the value of a normal random variable 1 2
Applications of the Normal Distribution We want to calculate probabilities and values for general normal probability distributions We can relate these problems to calculations for the standard normal in the previous section

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Applications of the Normal Distribution For a general normal random variable X with mean μ and standard deviation σ , the variable has a standard normal probability distribution We can use this relationship to perform calculations for X σ μ - = X Z
For example, if μ = 3 σ = 2 then a value of x = 4 for X corresponds to a value of z = 0.5 for Z Applications of the Normal Distribution 5 0 2 3 4 . z = - =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Because of this relationship Values of X  Values of Z then P ( X < x ) = P ( Z < z ) To find P ( X < x ) for a general normal random variable, we could calculate P ( Z < z ) for the standard normal random variable Applications of the Normal Distribution
Applications of the Normal Distribution This relationship lets us compute all the different types of probabilities Probabilities for X are directly related to probabilities for Z using the ( X μ ) / σ relationship

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Applications of the Normal Distribution A different way to illustrate this relationship a μ b X Z a – μ σ b – μ σ
Applications of the Normal Distribution σ μ - = x z With this relationship, the following method can be used to compute areas for a general normal random variable X

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/16/2008 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.

### Page1 / 25

Lecture_11,_Chap_7,__Sec_3 - Chapter 7 Section 3...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online