DW Co stock has an annual return mean and standard deviation

DW Co. stock has an annual return mean and standard deviation of 15.5 percent and 44 percent, respectively. What is the smallest expected loss in the coming year with a probability of 5 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the \"%\" sign in your response.)

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.05      
          
Then, using table or technology,          
          
z =    -1.644853627      
          
As x = u + z * s,          
          
where          
          
u = mean =    15.5      
z = the critical z score =    -1.644853627      
s = standard deviation =    44      
          
Then          
          
x = critical value =    -56.87355959

x = -56.87% [ANSWER]