Question

Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 4.9 percent and the standard deviation was 10.4 percent. What is the probability that your return on this asset will be less than –4.9 percent in a given year? Use the NORMDIST function in Excel® to answer this question

Answer 1

Answer:

0.500 is the probability that your return on this asset will be less than 4.9 percent in a given year.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  4.9 percent

Standard Deviation, σ = 10.4 percent

We are given that the distribution of returns on an asset is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(return on this asset will be less than 4.9 percent)

P(x < 4.9)

$P( x < 4.9) = P( z < \displaystyle\frac{4.9 - 4.9}{10.4}) = P(z < 0)$

Calculation the value from NORM-DIST function in Excel, we have,  

$P(x < 4.9) = 0.500 = 50.00\%$

0.500 is the probability that your return on this asset will be less than 4.9 percent in a given year.