Question

Assuming that the returns from holding small-company stocks are normally distributed, what is the approximate probability that your money will double in value in a single year? What about triple in value.

Many of my classmates have an expected return of 17.6% and a standard deviation of 34.8. Then they have the formula Prob(d>(200-17.6)/34.8 = prob. d>2.37
1-d>2.37=1-.991 = .009 chance of doubling.

I just need this problem explained to me. I'm not sure where all the numbers and information are coming from. Any help would be greatly appreciated.

Answer 1

normal distribution problem
I do not know where your mean (expected return) and sigma are coming from. I assume some text book.

Answer 2

Now if we assume a mean return of 17.6%
and a sigma of 34.8%
doubling is 100% which is 82.4% above mean and tripling is 200% which is 182.4% above mean
how many sigmas is 82.4?
82.4/34.8 =2.37 sigmas to double
how many sigmas is 182.4?
182.4/34.8 = 5.24 sigmas to triple
(note you used 200 where you should have used 100 in interpreting classmate results)

Answer 3

Now go to tables for normal distribution:
to be 2.37 sigmas above mean:
well I only have a rough table here. For z = 2.3, F(z) = .989
for z = 2.4, F(z) = .992
so about 99% is below 2.37 sigma above mean and we only have about a 100-99 or a 1 percent chance of doubling. (you probably have more accurate tables). You will need a very accurate table though to find any probability of exceeding 5.24 sigmas above mean