find the cutoff passing grade such that 83. 4% of those taking the test will pass

Question

The result of an exam score for a given class is normally distributed. If the mean score is 85 points and the standard devotion is equal to 20points

 

Answer 1

 

 

Per the normal table 83.4% = 0.8340 has a z-score of exactly z=0.97

 

 0.97 = (X-85)/20

 

0.97*20 + 85 = X

 

X = 104.4 <--- cutoff passing grade

 

So Prob( X<=104.4) = Prob ( z < (104.4-85)/20) = Prob (z < 0.97) = 0.8340 = 83.4%