Continuous Probability Distributions In this chapter, we’ll be looking at continuous probability distributions. A density curve (or probability distribution function) is a graph of a continuous probability distribution. It must satisfy these properties: 1.The total area under the curve must equal 1 2.Every point on the curve must have a vertical height (y-value) that is 0 or greater.

Uniform Distribution A Uniform Distribution (where every outcome is equally likely) has a density curve that looks like a rectangle.

Now, suppose that the time it takes me to do the dishes is uniformly distributed between 10.0 and 15.0 minutes. Notice that the area under the curve is 1.

Area and Probability There is a correspondence between probability and area. To find the probability that it will take me longer than 13 minutes to do the dishes, we find an area: Area = = 0.4 P(13 or more) = 0.4

Normal Distribution The normal distribution has a bell shaped curve. It’s a bit harder to find areas, but still: area under the curve corresponds to a probability.

Standard Normal Distribution The Standard Normal Distribution is a normal probability distribution with a mean of 0 and a standard deviation of 1.

Probabilities from z-Scores z-Score is the location on the horizontal axis Probability comes from the area under the curve. Note: We can only find probabilities for a range of z-scores (so we get an area).

Let’s find: P(z less than 1.47) = P(z < 1.47) P(z greater than –0.45) = P(z > -0.45) P(z between –1.12 and 0.74) = P(-1.12 < z < 0.74) 95 th percentile

Homework 5.2: 9, 13, 17, 29, 33, 37 For more practice: odds