I have been encountering this qns in qbank and i cant seem to understand how to derive the ans. An investment has a mean return of 15% and a standard deviation of returns equal to 10%. Which of the following statements is least accurate? The probability of obtaining a return: A) greater than 25% is 0.32. B) between 5% and 25% is 0.68. C) greater than 35% is 0.025. Your answer: A was correct! Sixty-eight percent of all observations fall within +/- one standard deviation of the mean of a normal distribution. Given a mean of 15 and a standard deviation of 10, the probability of having an actual observation fall within one standard deviation, between 5 and 25, is 68%. The probability of an observation greater than 25 is half of the remaining 32%, or 16%. This is the same probability as an observation less than 5. Because 95% of all observations will fall within 20 of the mean, the probability of an actual observation being greater than 35 is half of the remaining 5%, or 2.5%. ================================================ In the explanation, it states: Given a mean of 15 and a standard deviation of 10, the probability of having an actual observation fall within one standard deviation, between 5 and 25, is 68%. How to get the 1 standard deviation using the mean of 15 and standard deviation of 10. Do i memorize or there is a way to calculate? Thanks

This is nothing than the application of the normal distribution. Yes for the exam you are expect to memorize key values such is probability of 65, 85, 90, 99 I forgot what they are, but they are written somewhere in the LI curriculum. You will use them so much when you are doing mocks and questions. You will automaticlly memorize them

Just Remember, mean +/- Std = 68% mean +/- 2Std = 95% mean +/- 3Std = 99% So when return is 15% and std is 10%, the prob is 68% to obtain return between 5% and 25%, i.e. prob of greater than 25% is 1-.68 = .32 Prob of return between -5% and 35% is 95% Hope it is clear to u. Well, my question here is: why choice (b) is not correct ?

gulfcfa Wrote: ------------------------------------------------------- > This is nothing than the application of the normal > distribution. > Yes for the exam you are expect to memorize key > values such is probability of > 65, 85, 90, 99 > > I forgot what they are, but they are written > somewhere in the LI curriculum. > > You will use them so much when you are doing mocks > and questions. You will automaticlly memorize them The values u need to memorize are: 90% = 1.65 95% = 1.96 99% = 2.58