chance of losing money

[TheExpat]

Please explain the solution for this problem The expected return 10% , stdev 5% , the returns are normally distributed what is the chance of losing money?

 

[S2000magician]

What’s the probability that the return is less than 0%?
Sounds like it’s P(z < -2).

 

[TheExpat]

Still not get it can you give more explanation

 

[dwheats]

Look up the probability at z = -2 in the z-table.

 

[S2000magician]

TheExpat wrote:Still not get it can you give more explanation

Losing money means that the return is less than 0%.
0% = 10% – 2 × 5% = μ – 2σ.
Thus, P(loss) = P(return < 0%) = P(Z < -2).
Take your normal distribution with μ = 10% and σ = 5% and X = 0%, transform it into a standard normal distribution (μ = 0, σ = 1) and determine the z-value that corresponds to X = 0%; if you’ve done it correctly, it’ll be Z = -2.