Salaries at a large corporation have mean of 40000 and stdev

Salaries at a large corporation have mean of $40,000 and stdev of $20,000. What is the probability that the average of ten randomly selected employees is more than $50,000? We can use a Z-table to compute this probability.

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    50000      
u = mean =    40000      
n = sample size =    10      
s = standard deviation =    20000      
          
Thus,          
          
z =    1.58113883      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.58113883   ) =    0.0571
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