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Chapter 6 – “Random Variables” 6.1 – Discrete & Continuous Random Variables By the end of this section, you should Be aBle to do… • Calculate and interpret the standard deviation of a discrete random variable. • Compute probabilities using the probability distribution of a continuous random variable. Variance of any discrete random variable X: 𝜎𝑋2 = 𝑉𝑎𝑟ሺ𝑋ሻ = Standard deviation of any discrete random variable X: Be mindful of your notation! Example 6.7: What are typical Apgar scores (see page 349 for a description)? Consider the random variable X = Apgar Score. Compute the standard deviation of the random variable X and interpret it in context. Example 6.8: In an earlier example, we defined the random variable X to be the number of languages spoken by a randomly selected U.S. high school student. The table below gives the probability distribution of X: Compute the standard deviation of the random variable X and interpret this value in context. C.Y.U. – Page 355 A large auto dealership keeps track of sales made during each hour of the day. Let X = the number of cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the probability distribution of X is as follows: 1. Compute and interpret the mean of X. 2. Compute and interpret the standard deviation of X. Suppose we want to use our graphing calculators to randomly generate numbers between 0 and 1. Can we count them all? Our sample space is simply S = all numbers between 0 and 1. Continuous random variable X: The probability of any continuous event is Example 6.9: The weights of 3-year-old females closely follow a Normal distribution with a mean of 𝜇 = 30.7 pounds and a standard deviation of 3.6 pounds. Randomly choose one 3-yearold female and call her weight X. What is the probability that a randomly selected 3-year-old female weighs at least 30 pounds? Discrete vs. Continuous Random Variables (recap) Homework: Page 360 - 362 #14, 16, 17, 18, 22, 24, 26