Probability distribution Question?

Question

A financial analyst wanted to determine the mean annual return on mutual funds. A random sample of 60 returns shows a mean of 12%. If the population standard deviation is assumed to be 4%, estimate with 95% confidence the mean annual return on all mutual funds

Answer 1

What you want is the 95% confidence interval or the mean annual returns. This is simple.

Your sample size is 60. Therefore the standard deviation of the sample mean is

population standard deviation / sqrt(60) , See Central Limit Theorem.

Therefore mean standard deviation is 4/sqrt(60) = 0.5164

Also, refer to the Gaussian Distribution (Normal Distribution),
the 95% confidence interval is around 1.96 * standard deviation.

So, the confidence interval is
[4 - 1.96*0.5164 , 4 + 1.96*0.5164]

= [2.99 , 5.01], ie between 2.99% and 5.01%, or 4% +- 1.01