Unit 2 Density Curves and the Normal Distribution

Unit 2: Density Curves and the Normal Distribution Funky Figures 2. 1. 2

Example #1 A density curve consists of line segments connecting the points (0, 0), (1, 1) and (2, 0). a) Draw the density curve b) Verify is it a valid density curve c) Find the proportion of values that are higher than 1

Example #1 Solution A density curve consists of line segments connecting the points (0, 0), (1, 1) and (2, 0) 0 1 2

Example #1 Solution b) Verify is it a valid density curve Area = 1? 0 1 2

Example #1 Solution c) Find the proportion of values that are higher than 1 0 1 2

Example #2 A density curve consists of line segments connecting the following points: a) Draw the density curve b) Verify is it a valid density curve c) Find the proportion of values higher than. d) Find the proportion of values higher than.

Example #2 A density curve consists of line segments connecting the following points: a) Draw the density curve b) Verify is it a valid density curve c) Find the proportion of values higher than. d) Find the proportion of values higher than.

Example #2 Solution a) DRAW A PICTURE!! 0 ½ 1

Example #2 Solution b)Verify is it a valid density curve Area = 1! 0 ½ 1

Example #2 Solution b) Find the proportion of values higher than 0 ½ Answer: 1

Example #2 Solution b) Find the proportion of values higher than 0 ½ Answer: ¾ 1

In Video Quiz Consider the density curve starting at the origin bounded by the line y = 2 x. a) At what point would the line need to stop in order for it to be a valid density curve? b) What proportion of data is above 1? c) What proportion of data is below 0. 25? d) What proportion of data is above 0. 75?

In Video Quiz Solution a) The line would need to stop at (1, 2) for the area underneath the curve to be 1. 0 b) Area = 0 1 0 . 25 1 0 . 75 1

Wrap Up After this lesson you should be able to… o Draw a non-uniform density curve to represent a situation o Use a non-uniform density curve to answer questions about proportions of data.