The time to complete a manual task in a manufacturing operat

The time to complete a manual task in a manufacturing operation is considered a normally distributed random variable with mean of 0.50 minute and standard deviation of 0.05 minute. Find the probability that the average time to complete the manual task, after 49 repetitions, is than 0.465 minute.

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    0.465      
u = mean =    0.5      
n = sample size =    49      
s = standard deviation =    0.05      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -4.9      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -4.9   ) =    0.000000479183 [ANSWER]