\"A private equity firm is evaluating two alternative investments. Although the

Question

"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.

Explanation / Answer

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  

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