Suppose that the distribution of the number of items x produ

Suppose that the distribution of the number of items x produced by an assembly line during an 8-hr shift can be approximated by a normal distribution with mean value 140 and standard deviation 10. (Round your answers to four decimal places.)

(a) What is the probability that the number of items produced is at most 120?
P(x 120) =

Solution

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    120      
u = mean =    140      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    -2      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2   ) =    0.022750132 [ANSWER]