Empirical rule and standard deviation question?
In statistics, the empirical rule (also called the 68-95-99.7 rule) says that in a normal (bell-shaped) distribution, you can expect: 68% of the data to be within ±1 standard deviation of the mean 95% of the data to be within ±2 standard deviations of the mean 99.7% of the data to be within ±3 standard deviations of the mean Your number is 2 standard deviations *above* the mean. 105 + 13 + 13 = 131 --> 2 standard deviations above the mean But it isn't asking for the area around the mean. If it were, the answer from the empirical rule would be 95%. And if were asking for the values both below -2 and above 2, it would be 5% (because that's what is left). However, you only want the tail end to the right. You know that left *and* right is 5% and you also know the bell-shape is symmetric, so it is 2.5% on each side. Answer: The area that is above 2 standard deviations (using the empirical rule) is 2.5%
Captain Matticus, LandPiratesInc
(131 - 105) / 13 => 26/13 => 2 So, how much of the population is less than 2 standard deviations over the mean? http://www.z-table.com/ 0.9772 97.72% of the population has an IQ less than 131 1 - 0.9772 => 0.0228 2.28% of the population has an IQ of 131 or above