Normal Distributions

Normal Distributions - 4.3 NORMAL PROBABILITY DISTRIBUTIONS...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
4.3 NORMAL PROBABILITY DISTRIBUTIONS The Most Important Probability Distribution in Statistics
Background image of page 1

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

View Full DocumentRight Arrow Icon
A random variable X with mean μ and standard deviation σ is normally distributed if its probability density function is given by ... 71828 . 2 e and ... 14159 . 3 where x e 2 1 ) x ( f 2 x ) 2 / 1 ( = = π - π σ = σ μ - - Normal Distribution
Background image of page 2
The Shape of the Normal Distribution The normal distribution is bell shaped, and symmetrical around μ. μ y symmetrical? Let μ = 100. Suppose x = 110. 2 2 10 ) 2 / 1 ( 100 110 ) 2 / 1 ( e 2 1 e 2 1 ) 110 ( f σ - σ - - π σ = π σ = Now suppose x = 90 2 2 10 ) 2 / 1 ( 100 90 ) 2 / 1 ( e 2 1 e 2 1 ) 90 ( f σ - - σ - - π σ = π σ = 110 90
Background image of page 3

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

View Full DocumentRight Arrow Icon
Normal Probability Distributions The expected value (also called the mean ) μ can be any number The standard deviation σ can be any nonnegative number There are infinitely many normal distributions
Background image of page 4
The effects of The effects of μ μ and and σ σ How does the standard deviation affect the shape of f(x)? σ = 2 σ =3 σ =4 μ = 10 μ = 11 μ = 12 How does the expected value affect the location of f(x)?
Background image of page 5

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

View Full DocumentRight Arrow Icon
X 8 3 6 9 12 0 μ A family of bell-shaped curves that differ only in their means and standard deviations. µ = the mean of the distribution σ = the standard deviation µ = 3 and σ = 1
Background image of page 6
X 3 6 9 12 0 X 3 6 9 12 0 μ µ = 3 and σ = 1 μ µ = 6 and σ = 1
Background image of page 7

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

View Full DocumentRight Arrow Icon
X 8 3 6 9 12 0 μ X 8 3 6 9 12 0 μ µ = 6 and σ = 2 µ = 6 and σ = 1
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/10/2011 for the course BUS 350 taught by Professor Reiland during the Spring '08 term at N.C. State.

Page1 / 36

Normal Distributions - 4.3 NORMAL PROBABILITY DISTRIBUTIONS...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online