A sample average is 54 while a sample size is 159. If a population deviation is 19 estimate a true mean that should be accurate with a probability of 99%.
So I started with $(1-0.99)/2 = 1/200$ then I started to look in the Z-Table for the Z-Score. I came up with the value of 0.1841 which I am not sure is correct. After that I substracted $54-0.1841=53.8159$ and added $54+0.1841=54.1841$ to get that CI is (53.8159,54.1841). Is this correct, or am I missing the complete idea of the task?
Overlooking awkward terminology: A 99% confidence interval for the population mean $\mu$ is $\bar X \pm 2.576\frac{\sigma}{\sqrt{n}}.$ I got the interval $(51.9571, 56.0429),$ but you should check my arithmetic.