Statistics Problem!!!!

Question

consider that the historical return of an investment follows a normal distribution with a mean of 2000 dollars and a standard deviation of 300 dollars. what is the upper limit for which 60% of all investment return values are located given that the lower limit is at 1450 dollars?

Answer 1

 

Prob (  1450 < X < C ) = 0.60

 

Prob ( (1450-2000)/300 < z < C) = 0.60  <--- changes to z -score

 

Prob ( (-1.8333 < z < C ) = 0.60

 

Prob ( z < C) - Prob ( z < -1.83) = 0.60   <--- property of normal bell curve

 

Prob( z < C)  - 0.0336 = 0.60 <--- per normal table

 

Prob ( z < C) = 0.6336

 

C = 0.343 <-- per normal table (read in reverse)