Business Statistics Class A company that manufactures bookca

Business Statistics Class

A company that manufactures bookcases finds that the average time it takes an employee to build a bookcase is 10 hours with a standard deviation of 3 hours. A random sample of 49 employees is taken. What is the likelihood that the sample mean will be more than 12 hours?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    12      
u = mean =    10      
n = sample size =    49      
s = standard deviation =    3      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    4.666666667      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   4.666666667   ) =    0.00000153063 [ANSWER]