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Chapter 3 Modeling Distributions of Data 3.2 Normal Distributions Applications of Normal Distributions On the driving range, Tiger Woods practices his swing with a particular club by hitting multiple golf balls. When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 290 yards? What percent of Tiger’s drives travel between 305 and 325 yards? Solving Problems Involving Normal Distributions Step 1: State the problem in terms of the observed variable x. Step 2: Standardize and draw a picture. Standardize x to restate the problem in terms of a standard Normal variable z. Draw a picture to show the area of interest under the standard Normal curve. Step 3: Use the table. Find the required area under the standard Normal curve using Table A and the fact that the total area under the curve is 1. Step 4: Conclusion. Write your conclusion in the context of the problem. Example #1a – For us On the driving range, Tiger Woods practices his swing with a particular club by hitting multiple golf balls. When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 290 yards? Example #1b – For you On the driving range, Tiger Woods practices his swing with a particular club by hitting multiple golf balls. When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel between 305 and 325 yards? Guided Practice: Examples #2a - #3c Finding a Value, Given a Proportion •Sometimes we may want to find the observed value that corresponds to a given percentile. To do this, use Table A backwards. •Find the given proportion in the body of the table, read the corresponding z from the left column and top row, then “unstandardize” to get the observed value. •Huh? Let’s look at an example. Example #1c What distance would a ball have to travel to be at the 80th percentile of Tiger’s drive lengths? Guided Practice: Examples #2def, #3def