A stock market rises by an average of 10% a year and the standard deviation of returns is 6%. The probability of the stock market falling by more than 2% in a year is closest to:
A. 2.3%
B. 4.6%
C. 15.9%
D. 31.7%
I know I can just look up the answer but I don’t know how they got there. I need some help on this question, anyone? Thanks in advance
Let X be the random variable which describes the annual return. Given, XBar = +10% and sigma = +6%
The question is to find the probability, P (returns falling below 2%) = P (returns < -2%)
The z-score is calculated as z-score = ( X - XBar ) / sigma = ( -2 - 10 ) / 6 = -2
Assuming normal distribution, the probability P(returns < -2%) = P(z-score < -2) = 0.0228 = 2.28% or 2.3%
Is (A) the right answer?
should be correct
Yes, (A) is the right answer.
Thank you.