The owner of a computer repair shop has determined that thei

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will be less than $7000?

A) 0.8186

B) 0.5675

C) 0.4235

D) 0.1814

Solution

LEFT TAILED AREA          
          
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    7000      
u = mean =    7200      
n = sample size =    30      
s = standard deviation =    1200      
          
Thus,          
          
z =    -0.912870929      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -0.912870929   ) =    0.180655214 [closest to D. Probably, the difference is due to roundoff errors in tables. Again, the answer is OPTION D.]