The weekly amount spent for maintenance and repairs in a cer

The weekly amount spent for maintenance and repairs in a certain company has an approximately normal distribution with a mean of $600 and a standard deviation of $50. If $700 is budgeted to cover repairs for the next week, what is the probability that the actual cost will exceed the budgeted amount?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    700      
u = mean =    600      
          
s = standard deviation =    50      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132 [answer]