Consider a normal population distribution with the value of σ known. (a) what is the confidence level for the interval x ± 2.81σ/ n ? (round your answer to one decimal place.)

The confidence level would be 99.5%.

When we know the confidence level, we find the z-score by:
Dividing the CL by 100;
Subtracting this result from 1;
Dividing this result by 1;
Subtracting this result by 1.

Algebraically, this looks like:


Using a z-table (http://www.z-table.com), we see that a z-score of 2.81 results in an area under the curve of 0.9975, so we now have


To begin solving this, we will subtract 1 from both sides:


We will now multiply both sides by 2:


Subtract 1 from both sides:


Multiply both sides by 100:
CL = 99.5