Question

There are 12,000 stocks trading every day in the stock exchange. It’s known from the past that the returns to these stocks have a mean value of 10% per year, and a standard deviation of 20% per year.

A specific investor chooses to buy a random selection of 90 of these stocks for his portfolio. What’s the probability that the mean rate of return among these 90 stocks is greater than 8%?

Answer 1

for normal distribution z score =(X-μ)/σx
mean μ=	10
standard deviation σ=	20

std error=σx̅=σ/√n=20/√70 =

2.1082

probability =P(X>8)=P(Z>(8-10)/2.108)=P(Z>-0.95)=1-P(Z<-0.95)=1-0.1711=0.8289