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Unit 6 Section 6-4 – Day 1 Section 6-4 6-4: Applications of the Normal Distribution A standard normal distribution can often be used to solve practical application problems. In order to use the normal distribution, the variables must be normally (or approximately normally) distributed. In order to solve these problems, first translate the values of the variable into z values, then find the areas under the standard normal distribution. Hint: Drawing a picture will help! Section 6-4 Formula for a z-score Z = value – mean standard deviation Section 6-4 Example 1: The mean number of hours an American worker spends on the computer is 3.1 hours per workday. Assume the standard deviation is 0.5 hours. Find the percentage of workers who spend less than 3.5 hours on the computer. Assume the variable is normally distributed. Step 1: Draw a figure to represent the situation Step 2: Find the z value corresponding to 3.5 Step 3: Find the area Section 6-4 Example 2: Each month, an American household generates an average of 28 pounds of newspapers for garbage or recycling. Assume the standard deviation is 2 pounds. If a household is selected at random, find the probability of its generating… a) Between 27 and 31 pounds per month b) More than 30.2 pounds per month. Assume the variable is approximately normally distributed. Section 6-4 Example 3: The American Automobile Association reports that the average time it takes to respond to an emergency call is 25 minutes. Assume the variable is approximately normally distributed and the standard deviation is 4.5 minutes. If 80 calls are selected at random, how many will be responded to in less than 15 minutes? Section 6-4 Homework: Pg 316 Applying the Concepts (1 – 4) Exercises (1 – 4)