An accounting firm is planning for the next tax preparation

An accounting firm is planning for the next tax preparation season. From last year\'s returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 84 minutes with a standard deviation of 148 minutes. What is the probability that the mean completion time will be more than 122 minutes?

0.4949

0.0051

Approximately zero

0.3316

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    122      
u = mean =    84      
n = sample size =    100      
s = standard deviation =    148      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.567567568      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.567567568   ) =    0.005120741= 0.0051 [ANSWER, B]