Question

[Normal Distribution] Historically, the one-year returns follow approximately the normal distribution. The one-year return for the S&P 500 was +27% (that is, 0.27) and its standard deviation is 20% (that is, 0.2). What is the probability that a stock in the S&P 500 gained 30% or more last year?

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 0.27

S.d = 0.2

P(x>0.3)

Z = (0.3-0.27)/0.2 = 0.15

From z table, P(z>0.15) = 0.4404