An investment broker reports that yearly returns on common s

An investment broker reports that yearly returns on common stocks are normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent. (Round all k amounts to three decimal places. A negative sign should be used instead of the parentheses. For Z, use the inverse normal function and round to 3 decimal places, except when the percentile for part a is just 5, then you must interpolate. Percentage values should be entered without the (%) symbol.) (a) What percentage of yearly returns are at or below the 15th percentile of the distribution of yearly returns? What percentage are at or above the 15th percentile? Find the 15th percentile of the distribution of yearly returns.

Solution

(a) What percentage of yearly returns are at or below the 15th percentile of the distribution of yearly returns?

By definition, it is 15%.

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What percentage are at or above the 15th percentile?

It is 100-15 % = 85%. [ANSWER]

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Find the 15th percentile of the distribution of yearly returns.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.15      
          
Then, using table or technology,          
          
z =    -1.036      
          
As x = u + z * s,          
          
where          
          
u = mean =    12.4      
z = the critical z score =    -1.036      
s = standard deviation =    20.6      
          
Then          
          
x = critical value =    -8.9416% [ANSWER]