Question

The mean of a sample of size 20 from a normal population with standard deviation 8 was found to be 81.2. Find a 90% confidence interval for the population mean.

Answer 1

The 90% confidence interval for the population mean is found from:
\[\large \bar {x}-1.645\frac{\sigma}{\sqrt{n}}< \mu <\bar{x}+1.645\frac{\sigma}{\sqrt{n}}\]
Now you just need to plug in the given values.

Answer 2

Thanks @kropot72

But how did you get the 1.645 here.. I am new to this topic :(

Answer 3

It comes from the fact that \(P(Z>1.645)=0.05\). This means 1.645 is a critical value for the 90% CI.