help will rate thank you The Economic Policy Institute repor

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The Economic Policy Institute reports that the average entry-level wage for male college graduates is $21.95 per hour and for female college graduates is $19.82 per hour. The standard deviation for male graduates is $3.87 and for female graduates is $2.54. Assume wages are normally distributed.  

If 50 male graduates are chosen, find the probability the sample average entry-level wage is at least $21.37.

Solution

Here, as 50 males are used, then we use the data for males.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    21.37      
u = mean =    21.95      
n = sample size =    50      
s = standard deviation =    3.87      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.059746597      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.059746597   ) =    0.855370051 [ANSWER]