Unit 6a-1

Unit 6a-1 - Continuous Distributions Distributions...

This preview shows pages 1–17. Sign up to view the full content.

Continuous Continuous Distributions Distributions

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

View Full Document
Continuous random variables Continuous random variables Are numerical variables whose values fall within a range or interval Are measurements Can be described by density curves
Density curves Density curves Are always on or above on or above the horizontal axis Has an area exactly equal to one equal to one underneath it Often describes an overall distribution Describe what proportions proportions of the observations fall within each range of values

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

View Full Document
Unusual density curves Unusual density curves Can be any shape Are generic continuous distributions Probabilities are calculated by finding the area under the finding the area under the curve curve
1 2 3 4 5 .5 .25 P(X < 2) =   ( 29 25 . 2 25 . 2 = How do you find the area of a triangle?

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

View Full Document
1 2 3 4 5 .5 .25 P(X = 2) = 0 P(X < 2) = .25 What is the area of a line segment?
In continuous  distributions,         P( P( X X < < X X < < 2) 2)  are the  same answer. Hmmmm… Is this different than discrete distributions?

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

View Full Document
1 2 3 4 5 .5 .25 P(X > 3) = P(1 < X < 3) = Shape is a trapezoid – How long are the bases? ( 29 2 2 1 h b b Area + = .5(.375+.5)(1)=.4375 .5(.125+.375)(2) =.5 b 2 = .375 b 1 = .5 h = 1
1 2 3 4 0.25 0.50 P(X > 1) = .75 .5(2)(.25) = .25 (2)(.25) = .5

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

View Full Document
1 2 3 4 0.25 0.50 P(0.5 < X < 1.5) = .28125 .5(.25+.375)(.5) = . 15625 (.5)(.25) = .125
Special Continuous Distributions

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

View Full Document
Uniform Distribution Uniform Distribution Is a continuous distribution that is evenly (or uniformly) distributed Has a density curve in the shape of a rectangle Probabilities are calculated by finding the area under the curve ( 29 12 2 2 2 a b b a x x - = + = σ μ endpoints of the uniform  distribution How do you find the area of a rectangle?
4.98 5.04 4.92 The Citrus Sugar Company packs sugar in bags labeled 5 pounds. However, the packaging isn’t perfect and the actual weights are uniformly distributed with a mean of 4.98 pounds and a range of .12 pounds. a)Construct the uniform distribution above. How long is this   rectangle? What is the height of this rectangle? What shape does a uniform distribution have? 1/.12

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

View Full Document
What is the probability that a randomly selected bag will weigh more than 4.97 pounds? 4.98 5.04 4.92 1/.12 P(X > 4.97) = .07(1/.12) = .5833 What is the length of the shaded region?
Find the probability that a randomly selected bag weighs between 4.93 and 5.03 pounds. 4.98 5.04 4.92 1/.12 P(4.93<X<5.03) = .1(1/.12) = .8333 What is the length of the shaded region?

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

View Full Document
The time it takes for students to drive to school is  evenly distributed with a minimum of 5 minutes and  evenly distributed with a minimum of 5 minutes and  a range of 35 minutes. a range of 35 minutes.
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/09/2011 for the course STATS 221 taught by Professor Nielson during the Fall '10 term at BYU.

Page1 / 44

Unit 6a-1 - Continuous Distributions Distributions...

This preview shows document pages 1 - 17. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online