Continuous Random Variables
Day 54 - Lesson 6.1
Calculate and interpret the standard deviation of a discrete random variable.
Use the probability distribution of a continuous random variable (uniform or Normal) to calculate the probability of an event.
Activity: How Much Do You Get Paid?
Before class, you will need to write down student wages on slips of paper. The values are 1, 5, 7, 10, 15, and 25 dollars per hour. You should have a different number of slips of paper for each value. Put them in a hat and have students randomly select their wage as they come into class. Students who get $25 per hour will be ecstatic, while those getting only $1 will be totally bummed. We will use this “hourly wage” context for this lesson, as well as the first lesson in 6.2.
Students start the activity by calculating the mean of a discrete random variable (review from yesterday). The activity then walks students through the calculation of the standard deviation formula for a discrete random variable. We think it is worthwhile for students to work through this calculation one time and only one time. It will remind them that standard deviation is a measure of the “typical distance from the mean” and that we must use weighting when dealing with a discrete random variable. In the end, students will use the TI-83/84 calculator to find standard deviation of a discrete random variable (put X values in List 1 and probabilities in List 2, the do 1-Var Stats L1, L2).
Next, students investigate what happens when wages are assigned from a uniform distribution. They should recognize that probabilities can be calculated by finding areas.
Normal Distribution Calculations (Review)
Another very important idea in this lesson is finding area under a Normal distribution. A Normal distribution is, in fact, a continuous random variable. Students learned how to do this back in Lesson 2.2–Will Marty Make it Back to the Future?
In this lesson, students will do Normal distribution calculations in the Check Your Understanding. Be sure that you maintain the same expectations for work that you did back in Chapter 2. This will help students when they have to calculate a z-test statistic in Chapter 9.
Picture of the normal curve. Must be labeled N(mean, SD), the center labeled with the mean, and then the shaded area of interest.
Formula for a z-score, then numbers plugged in.
Find correct z-score and then use Table A to turn it into an area.