finding z value for confidence interval without standard deviation

Question

I am told to find the z value corresponding to the confidence interval level of 80.3% for the population mean where the sample size is n = 40. I am looking at the formula and it seems like I need the standard deviation. How would I go on about solving this without a standard deviation?

Answer 1

The $z$-value is a normalized value and is unrelated to the sample size or the s.d.

I'm going to suppose you are using a 2-tail Z-test.

We know that $$2P(Z\ge z)=1-0.803$$ Since $Z\sim N(0,1)$,we have $$z\approx1.29015$$