From a normally distributed population a simple random sample of size 30 is taken the mean of the sample is 144 and the standard deviation of the sample is 12 which interval is a 99% confidence interval for the population mean

The confidence interval is (138.36, 149.64) or .

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 corresponds with a z-score between 2.57 and 2.58; since both are equally distant from 0.995, so we use the one directly between them: 2.575

Now we calculate the confidence interval by:

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