Hi guys,

I’ve ran into a few problems that use different formulas to compute the Confidence interval and the Z score.

Please refer to the question:

**Ex:** Assume that the equity risk premium is normally distributed with a population mean of 6% and a population std. deviation of 18%. Over the last four years, equity returns (relative to the risk free rate) have averaged -2.0%. You have a large client who is very upset and claims that results this poor should never occur. Evaluate your client’s concerns.

**A**. Construct a 95% confidence interval around the population mean for a sample of four year returns.

**B**. What is the probability of a -2.0 percent or lower average return over a four year period?

**For the question A,** they use the below formula

However, I dont understand why they use the population mean to compute the confidence interval. Don’t we use the point estimate (sample mean)?

**For the question B,**

The answer used the equation “z = (observation - population mean)/(Std error)”

where std error = (std deviation/Sqrt(population size)) to compute the z score while I used the first equation [(z = observation - population mean)/ std deviation]

How would I know which one to use? they gave significantly different answers.

I’m very grateful for your help!!