The average annual salary for all US teachers is 47750 If th

The average annual salary for all U.S. teachers is $47,750. If the standard deviation is $5680, find the probability that the mean salary of 25 randomly selected teachers is less than $46,000

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    46000      
u = mean =    47750      
n = sample size =    25      
s = standard deviation =    5680      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.540492958      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.540492958   ) =    0.061720119 [answer]