A private equity firm is evaluating two alternative investme

\"A private equity firm is evaluating two alternative investments. Although the returns are random, each investment’s return can be described using a normal distribution. The first investment has a mean return of $2,000,000 with a standard deviation of $125,000. The second investment has a mean return of $2,275,000 with a standard deviation of $500,000.\"

\"a. How likely is it that the first investment will return $1,900,000 or less?
b. How likely is it that the second investment will return $1,900,000 or less?
c. If the firm would like to limit the probability of a return being less than $1,750,000, which investment should it make?\"

Please explain using the Normal Distribution Table and the Bell Shapes, as well. Thanks.

Solution

a)
Mean ( u ) =2000000
Standard Deviation ( sd )=125000
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P(X > 1900000) = (1900000-2000000)/125000
= -100000/125000 = -0.8
= P ( Z >-0.8) From Standard Normal Table
= 0.7881                  
P(X < = 1900000) = (1 - P(X > 1900000)
= 1 - 0.7881 = 0.2119                  
b)
Mean ( u ) =2275000
Standard Deviation ( sd )=500000
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 1900000) = (1900000-2275000)/500000
= -375000/500000 = -0.75
= P ( Z >-0.75) From Standard Normal Table
= 0.7734                  
P(X < = 1900000) = (1 - P(X > 1900000)
= 1 - 0.7734 = 0.2266