Here is the blurb: 10. An exchange rate has a given expected future value and standard deviation. A. Assuming that the exchange rate is normally distributed, what are the probabilities that the exchange rate will be at least 2 or 3 standard deviations away from its mean? I saw the solution, and makes no freaking sense. Can someone please explain the steps of how they got to the solution? Thanks!

I assume you are not looking for the approx solution: 1 - 95% = 5% lie at least 2sd away and 1 - 99% = 1% lie at least 3sd away. The exact value when seen from a z table against 2.00 SD away is .9772 i.e. 97.72% so 1-97.72% = 2.28% values lie in the right tail. Then 2.28% values must be in the left tail too. Total 4.56% values will lie at least 2 SD away from the mean. (Or we can say that the probability is .0456) Similarly for 3SD.

Thanks, anish. I didnâ€™t realize the problem was asking for the probability. I was over-analyzing the problemâ€¦ I was like, 2sd corresponds to 95%, which means 2.5% in each tail. Which means I need to look up .9750.