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Session Packet #3 Supplemental Instruction Iowa State University Leader: Carly Course: Stat 226 Instructor: Date: 2/4/13 Opening Activity: True/False Quiz For questions 1-15, answer true or false. If the statement is false, change it in a way that makes it true. Try to complete this quiz on your own without using your notes. ____ 1.) A statistical model is a breakdown of variation into a predictable pattern and the remaining variation. ____ 2.) Adding the probabilities associated with all outcomes of a random event yields 1. ____ 3.) Statistical models are adequate if they predict reality exactly. ____ 4.) A random variable describes the probabilities for an uncertain, past numerical outcome of a random process. ____ 5.) A random variable that takes on any value in an interval is called a discrete random variable. ____ 6.) The Probability Distribution of a Random Variable is a function that assigns probabilities to each possible outcome of the random variable. ____ 7.) The area under any density curve is always equal to 1. ____ 8.) Every normally distributed random variable follows a probability distribution that is characterized by the mean µ and the variance σ2. ____ 9.) The larger the σ2, the less variability in our data. ____ 10.) To denote that a variable follows a normal distribution, we use X~N(µ,σ2). ____ 11.) The normal distribution is symmetric about its variance σ2. ____ 12.) The 68-95-99.7 Rule, also known as the Empirical Rule, says that approximately 68% of the data in a normal distribution fall within a range of (µ-2σ, µ+2σ). ____ 13.) 13.5% of the data in a normal distribution will be between µ+σ and µ+2σ, according to the Empirical Rule. ____ 14.) The standard normal distribution has a mean of 0 and a variance equal to 1. ____ 15.) The lifespan of U.S. citizens follows a normal distribution with µ = 75 and a standard deviation of 2 years. The middle 95% of all U.S. citizens live between (75 – 2*(2)2) and (75+2*(2)2). 1060 Hixson-Lied Student Success Center 515-294-6624 [email protected] http://www.si.iastate.edu Labeling Activity: The Normal Distribution Model On the figure of the normal distribution model below, label each tick mark on the x-axis, the percentages associated with the Empirical Rule, and the percentages that represent the areas underneath the curve. Probability Activity: The Normal Distribution After finishing school, you decide to open a sunglass-selling stand. Your stand is only open during the summer. You know that based on other sunglass selling stands in the area, that the overall summer sales of sunglasses for this area is approximately normally distributed with a mean of 500 sunglasses and a standard deviation of 65 sunglasses. Assuming your stands’ sales will follow the same distribution, use the 68-95-99.7 Approximation Rule to find the answers to the following: What is the proper notation for this distribution? What is the probability that you sell more than 695 sunglasses? Your goal for the first summer is to sell as many sunglasses as the middle 95% of all such stands. Specify the range in which the number of glasses that you sell over the summer has to fall inside. What price must you charge to sell enough sunglasses to fall at the 2.5th percentile but still make at least $9,250? Closing Topic: Study Strategy Your first Statistics 226 exam is in two and a half weeks. It is time to start thinking about what study strategies work best for you. One option is to create checklists. List reading assignments, major ideas, definitions, and formulas. Here is an example of a checklist of what you have learned thus far in Chapter 12: Definition of Statistical Model Definition of Random Variable Continuous Random Variable vs. Discrete Random Variable (plus examples) Fundamental Properties for Probability (2 of them) Probability Notation Definition of Probability Distribution of a Random Variable Properties of a Normal Distribution of a Random Variable (mean, variance, shape, area) Definitions of Mean and Variance Notation of a Normal Distribution 68-95-99.7 Rule (Empirical Rule/ Approximation Rule) The Normal Distribution Model (slide 16) Remember, this checklist is not an all-inclusive review sheet. It is merely a to-do list. Try going back in your notes to make a check-list for Chapters 1-4. Once you’ve created your check list, go through each item in depth in preparation for your exam.