The Economic Policy Institute reports that the average entry

The Economic Policy Institute reports that the average entry-level wage for male college graduates is $22.61 per hour and for female college graduates is $18.87 per hour. The standard deviation for male graduates is $3.98 and for female graduates is $3.22. Assume wages are normally distributed.

Q1.If 29 female graduates are chosen, find the probability the sample average entry-level wage is at least $19.68.

Solution

Q1.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    19.68      
u = mean =    18.87      
n = sample size =    29      
s = standard deviation =    3.22      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.354653259      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.354653259   ) =    0.087764028 [ANSWER]