MathBench > Statistics

Normal Distributions and the Scientific Method

Exploring the Fish2Whale Distribution

Here is a picture of the distribution of fish sizes for the treatment (Fish2Whale) group. Notice that, if the fish follow an IDEAL normal distribution, we can make a lot of statements about their size distribution (i.e., what percentage of fish are in what size group):

normal distribution: 68-95-99.8% rule

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Recall that when we fed the fish Fish2Whale, the average final length was 25 cm, with a standard deviation (SD) of 3 cm.

what percentage of fish fall between 25 and 28 cm? %

what percentage of fish fall between 22 and 28 cm? %

what percentage of fish are longer than 28 cm? %

what percentage of fish are between 28 and 31 cm? %

Answers: 34, 68, 16, 13.5

We can do the same thing with ANY ideal normal distribution, such as the height of adult women, or the SAT scores of incoming freshmen...


This is sometimes abbreviated as "the 68-95-99.8% rule", or (rather inaccurately) "the 2/3 rule", since approximately 2/3 of the observations lie within 1 SD of the mean.