The power cells which fit a certain type of digital watch op

The power cells which fit a certain type of digital watch operate for a mean of 379 days with a standard deviation of 35 days. The manufacturer delivers the cells to retailers in lots of 100. What percent of the lots will operate with a mean of a year or more? 100% 4% 50% 150%

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    365      
u = mean =    379      
n = sample size =    100      
s = standard deviation =    35      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -4      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -4   ) =    0.999968329 or around 100% [ANSWER, OPTION 1]