# 8: Overlapping Distributions

In the applet below, you are seeing the distributions of fish size for treatment (Fish2Whale)
and control (normal fishfood) on the same graph. And you can see that they overlap quite a bit,
as you would expect based on the calculations we made on the previous screens.

In fact, about one-third of EACH group falls between the 22 and 25 cm mark. This will make it
difficult (not necessarily impossible) to prove that Fish2Whale is better than normal fishfood.
However, we’re not going to go there in this module. I just want you to play with this applet
a bit, and answer the questions below.

[swf src=”http://mathbench.org.au/wp-includes/swf/demoNormDist2Stage_Scene_1.swf” width=”700″ height=”700″]

Your boss decides that Fish2Whale needs to be improved — but he doesn’t want to spend any more
money than he has to. He wants to make Fish2Whale just better enough that the two distributions
overlap by only 5%. Your job is to find how to do this.

1. Do you think it is possible to change MEAN fish growth enough (while keeping the SD fixed) to achieve only 5% overlap? (Just eyeball the overlap, don’t worry about quantifying it).
2. Do you think it is possible to change the STANDARD DEVIATION of fish growth enough
(while keeping the mean fixed) to achieve only 5% overlap?