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):
Fill in the Blanks
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?
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…
- 68% of the normal distribution falls within 1 SD of the mean
- 95% falls within 2 SDs of the mean
- 99.8% falls within 3 SDs of the mean
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.