Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 18. Using the empirical rule, what percentage of IQ scores are between 86 and 122?
+223 The empirical rule basically states that 68% of the data falls within one standard deviation from the mean, 95% of the data falls within two standard deviations from the mean, and 99.7% of the data falls within three standard deviations from the mean.
So to find the percentage of IQ scores between 86 and 122, you need to find how far each of these numbers is from the mean in terms of the standard deviation. Luckily, if you subtract the standard deviation from the mean, you receive 86, and if you add the standard deviation to the mean, you receive 122. This means that both of these numbers are within one standard deviation from the mean meaning according to the empirical rule, that means 68% of the IQ scores are between 86 and 122.
