AP Statistics Tuesday, 05 January 2016 OBJECTIVE TSW investigate the properties of continuous distributions. You may sit anywhere close to the FRONT OF THE ROOM. REMINDER: My website:

2 Continuous Distributions

3 Continuous Distribution – (Continuous Random Variables) Are numerical variables whose values fall within a range or interval Are measurements Can be described by density curves

4 Density Curve on or aboveIs always on or above the horizontal axis equal to oneHas an area exactly equal to one underneath it Often describes an overall distribution proportionsDescribes what proportions of the observations fall within each range of values

5 Unusual Density Curves Can be any shape Are generic continuous distributions finding the area under the curveProbabilities are calculated by finding the area under the curve

6 P(X < 2) = How do you find the area of a triangle?

7 P(X = 2) =0 P(X < 2) =0.25 What is the area of a line segment?

8 P(X < 2) & P(X < 2) In continuous distributions, P(X < 2) & P(X < 2) are the same answer. Hmmmm… Is this different than discrete distributions?

9 P(X > 3) = P(1 < X < 3) = Shape is a trapezoid – How long are the bases? 0.5( )(1)= ( )(2) =0.5 b 2 = b 1 = 0.5 h = 1

10 P(X > 1) =.75.5(2)(.25) =.25 (2)(.25) =.5

11 P(0.5 < X < 1.5) = ( )(.5) = (.5)(.25) =.125

Assignment WS Unusual Density Curves is due tomorrow, Wednesday, 06 January