Question

We want to estimate the population mean within 5, with a 99% level of confidence. the population standard deviation is estimated to be 15. how large a sample is required?

Answer 1

A sample size of 60 is required.

We use the formula
$n=(\frac{z*\sigma}{E})^2$

We first find the z-score associated with this level of confidence:
Convert 99% to a decimal:  99/100 = 0.99
Subtract from 1:  1-0.99 = 0.01
Divide by 2:  0.01/2 = 0.005
Subtract from 1:  1-0.005 = 0.995

Using a z-table (http://www.z-table.com) we see that this value is equally distant from 2.57 and 2.58; therefore we will use 2.575:

$n=(\frac{15(2.575)}{5})^2=59.68\approx60$