Normal Distributions Statistics Lesson 15 Individual Preparation 1. In a previous lesson, we discussed discrete random variables (such as the roll of a die). The graph of a probability distribution for a discrete random variable is very similar to a histogram. The x-axis shows all of the possible outcomes, and the y-axis shows the probability of each outcome. The graph of the discrete probability distribution for rolling a fair 6-sided die is provided below. Probability 2 3 4 6 Die roll a. What do you notice about the area of the big rectangle in the graph? notice that all the levels are equal b. What do we call the shape of this distribution? Uniform 2. Now let's learn more about continuous random variables (such as height, wait-time, etc.) and their graphs called density curves. Like a discrete probability distribution, a density curve must meet two requirements: * Every point on the curve must have a vertical height greater than or equal to O. * The total area under the curve must equal 1. a. Since the sum of the probabilities in a sample space has to equal one, we now make the link between probability and the area under a density curve (or graph of a continuous probability distribution). Find the area of each shaded rectangle in the examples below. 1.1451 3.16855. Now, find the area to the left of z = 0.73. Since the z-score is positive this time, we need to look at the page of the Z Table containing the positive z-scores. You may also use the normalcdf function on your calculator. a. P(z 0.73) = 0.2326 7. How would you find the area between z = -1 and z = 0.73? a. To the right, draw your own standard normal distribution shade the area in consideration, and then find the area between z = -1 and z = 0.73. (This is the probability we are looking for). P (- 1