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Consider an investment whose return is normally distributed with a mean
of 10% and a standard deviation of 5%. 
Justify which statistics methodology needs to be used in the above context and
a) Determine the probability of losing money.
b) Find the probability of losing money when the standard deviation is equal to 10%.
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You need to find the area under the specified normal curve on the left of the zero value
(where the investment return is negative). This area is the desired probability.
It can be done in many different ways, using the normal distribution cumulative function.
For example, you can get the answer using calculator TI-83 or TI-84 in this format
z1 z2 mean SD
(a) P = normalcdf(-9999, 0, 0.1, 0.05) = 0.0228 (rounded). ANSWER
(b) P = normalcdf(-9999, 0, 0.1, 0.1) = 0.1587 (rounded). ANSWER
Solved.
For another way to solve the problem, go to web-site https://onlinestatbook.com/2/calculators/normal_dist.html
and use there free of charge online calculator, specially developed for such problems.
Input the mean value 0.1 (which represents 10%) and the standard deviation value 0.05 (which represents 5%);
input 0 in the window "Below"; then click "Recalculate".
You will get the ANSWER 0.0228 in the window "Probability".
The auxiliary plot will show you the area of the interest.
So, part (a) is just solved this way.
Next, solve part (b) similarly.
If you are a beginner in such problems, I recommend you to play with this online solver.
After that, you will understand much better what is going on and how the things work.
