On the SAT the average Writing score is 490 points and the a

On the SAT, the average Writing score is 490 points and the average Mathematics score is 520 points. The standard deviation is 80 points on each part of the test. Now suppose 55 test takers are selected.

2% of the time the sample average Mathematics score should be less than what?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.02      
          
Then, using table or technology,          
          
z =    -2.053748911      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    520      
z = the critical z score =    -2.053748911      
s = standard deviation =    80      
n = sample size =    55      
Then          
          
x = critical value =    497.8458043   [ANSWER]