Standard deviation and empirical rule?
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.38. Using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.7?
Answers
Captain Matticus, LandPiratesInc
(3.7 - 2.56) / 0.38 => 1.14 / 0.38 => 3 (1.42 - 2.56) / 0.38 => -1.14 / 0.38 => -3 http://www.z-table.com/ You're ranging from -3 standard deviations from the mean to +3 standard deviations from the mean. https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule That includes 99.7% of the population Using the Z-table, we see that 0.0013 are below -3 sd and 0.9987 are below +3 sd. 0.9987 - 0.0013 => 0.9974 => 99.74%
alex
99.7%
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