## Trending News

# How do I find the minimum sample mean needed to estimate a population mean to within 2.5cm with 99%confidence?

I can not figure out how to do this, can someone PLEASE help! :)

Question: The typical mean volume of the white matter in the cerebrum of a 2 year old is 250cm3 with a standard deviation of 4.5cm3.

What would be the minimum sample needed to estimate the population mean volume of cerebellum white matter to within 2.5cm with 99% confidence?

### 1 Answer

- 9 years agoFavorite Answer
So here is the information we have:

x bar: 250

std.deviation=4.5cm3

99% confidence

We would first use the 99% confidence level to find z*; We could use a calculator and do -invnorm((1-.99)/2), which is located under the Distributions menu, or use a table. I happen to have my calculator handy, so I used it and got a z* value of 2.576.

Margin of error (which is given as 2.5cm) is defined as z* multiplied by std.deviation/√n.

Thus, we can set up the equation 2.5=2.576(4.5/√n).

Now it's just a matter of simple algebra!

Divide both sides by 2.576, and you will get:

.970=4.5/√n

Now just cross multiply and isolate n on its own side of the equation

4.5/.970=√n

Square both sides, and you get 21.522, but since there is no way we can take a sample of a half-person, and truncating would cause us to miss our target for the margin of error, we would round up, and say that our minimum sample size is 22.

Hope this helps! :-)