The returns on stocks are normally distributed with a mean o

The returns on stocks are normally distributed with a mean of 10 and a standard deviation of 2. A random sample of 9 stocks are chosen from the portfolio of stocks.

What is the probability the average return on the portfolio is more than 11?

Solution

Normal Distribution
Mean ( u ) =10
Standard Deviation ( sd )=2
Number ( n ) = 9
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 11) = (11-10)/2/ Sqrt ( 9 )
= 1/0.667= 1.5
= P ( Z >1.5) From Standard Normal Table
= 0.0668