Ascientist wishes to estimate the average depth of a river. he wants to be 99% confident that the estimate is accurate within 2 feet. from previous studies, the standard deviation of the depths measure was 4.33 feet. how large a sample is required.

The sample size should be 31.

We use the formula



To find the z-score for 99% confidence:
Convert 99% to a decimal = 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 can see that this value falls between 2.57 and 2.58; we will use 2.575.  Using this for z, our value for σ and our value for E, we have: