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 28 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 - 1 SD and the mean + 1 SD.
I think I have the answer: 68%
(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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