Answer: a. 2.44%
b. 0.001070%
Explanation:
Given: The returns from an asset are normally distributed with
[tex]\mu=\text{ 13.6 percent and }\sigma=\text{43.86 percent.}[/tex]
Let x be the percentage value of return.
a. Double in value in a single year i.e. 100% return.
z-value = [tex]\dfrac{x-\mu}{\sigma}[/tex]
[tex]=\dfrac{100-13.6}{43.86}=1.97[/tex]
Required probability = Right-tailed probability for Z = 1.97
= 0.0244 [By p-value calculator]
= 2.44%
b. Triple in value in a single year i.e. 200% return.
z-value = [tex]\dfrac{x-\mu}{\sigma}[/tex]
[tex]=\dfrac{200-13.6}{43.86}=4.25[/tex]
Required probability = Right-tailed probability for Z =4.25
= 0.0000107 [By p-value calculator]
= 0.001070%