If the average length of a particular type of shoulder bolt

If the average length of a particular type of shoulder bolt is 1.5 inches, and a sample standard deviation is 0.05 inches, estimate how many shoulder bolts exceed 1.6 inches in a production run of 1000 bolts. 10 5 15 23

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    1.6      
u = mean =    1.5      
          
s = standard deviation =    0.05      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132

Thus, we expect 0.022750132*1000 = 22.8 or 23 bolts. [ANSWER, D]