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Statistics Notes: 7.3 Applications of Normal In Context 7.3 Applications of the Normal Distribution. Also known as finding areas under the normal distribution curve. Formula to find a Zscore? Since 1900, in California, the magnitude of earthquakes that measure 0.1 or higher on the Richter Scale is distributed approximately normally with a mean of 6.2 and a standard deviation of 0.5. What is the probability that a randomly selected earthquake has a magnitude less than 6.4? What is the probability that a randomly selected earthquake has a magnitude of 5.8 or higher? What is the probability that a randomly selected earthquake has a magnitude between 5.6 and 7.1? The great San Francisco Earthquake of 1906 has a magnitude of 8.25. Is an earthquake of this magnitude unusual? 1 Statistics Notes: 7.3 Applications of Normal In Context Solve the Zscores formula for X. Since 1900, in California, the magnitude of earthquakes that measure 0.1 or higher on the Richter Scale is distributed approximately normally with a mean of 6.2 and a standard deviation of 0.5. Determine the 40th percentile magnitude. What is the weakest earthquake of the most destructive 1% of all earthquakes? What range of magnitudes delineate the middle 85% of earthquakes? HW: p411#1 7odd, 11, 17, 19, 21, 27, 29 2