There are two major tests of readiness for college the ACT a

There are two major tests of readiness for college: the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly Normal with mean = 20.9 and standard deviation = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean = 1026 and standard deviation = 209.

Reports on a student\'s ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one.

Tanya scores 1316 on the SAT. What is her percentile (± 1)? ___%

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    1316      
u = mean =    1026      
          
s = standard deviation =    209      
          
Thus,          
          
z = (x - u) / s =    1.387559809      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   1.387559809   ) =    0.917364436 = 91.74% [ANSWER]