74 An analysis of the grades on the first test in History 10

74. An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10 percent of the test grades. What is the dividing point between an A and a B grade? A) 80 B) 85 C) 90 D) 95 Answer: B Please work this out for me step- by- step.

Solution

This grade has a left tailed area of 1-0.10 = 0.90.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.9      
          
Then, using table or technology,          
          
z =    1.281551566      
          
As x = u + z * s,          
          
where          
          
u = mean =    75      
z = the critical z score =    1.281551566      
s = standard deviation =    8      
          
Then          
          
x = critical value =    85.25241252 = 85 [ANSWER, B]