# Testing Fish2Whale

Recall that, after an angry exchange of emails, the winning procedure for testing Fish2Whale fishfood was:

- Feed normal fish food to one group of fish (the control group) and
- Feed Fish2Whale to another group of fish (the treatment group) and
- See which group grows longer in length.

Here is the data your lab got:

Control group **mean length** 22 cm, **SD** 3 cm

Treatment group **mean length** 25 cm, **SD** 3 cm

### What percentage of the control group fish are between 22 and 25 cm?

(To make this problem interactive, turn on javascript!)

- I need a hint ... : Remember that 68% of a normal population falls between plus and minus 1 SD.

- ...another hint ... : The control group mean plus 1 SD = 22+3 = 25

- ...another hint ... : This is the same as asking what percentage of the population
is between the mean and the mean + 1 SD.

- ...another hint ... : A normal distribution is symmetrical.

#### I think I have the answer: 34% (half of 68%, since 22 to 25 is the same as the mean and the mean + 1 SD)

### What percentage of the treatment group fish are between 22 and 25 cm?

(To make this problem interactive, turn on javascript!)

- I need a hint ... : This is the same as asking what percentage of the population is between the mean and the mean + 1 SD.

#### I think I have the answer: 34%

(The numbers worked out quite easily here since I chose exactly the mean and the mean plus 1 SD as the range of interest. However, there are tables which allow you to make the same calculation for any range you're interested in. We won't cover them here.)

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