show work A firms stock has an expected annual return of 22

* show work* A firm\'s stock has an expected annual return of 22% and an annual standard deviation of returns equal to 33%. If the stock\'s returns are normally distributed you should expect to get a return greater than 71.5% OR less than -27.5% about once every

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    -27.5      
x2 = upper bound =    71.5      
u = mean =    22      
          
s = standard deviation =    33      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.5      
z2 = upper z score = (x2 - u) / s =    1.5      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.066807201      
P(z < z2) =    0.933192799      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.866385597      

Thus, those outside this interval is the complement =    0.133614403      

Thus, we expect this once every 1/0.133614403 = 7.484223089 years. [ANSWER]