Problem Solving

At Capetown college out of the 400 students taking Psychology 101 received an average score of 76 on the final exam, and the scores had a normal distribution. The bottom 16 percent of scores will receive a failing grade. If 8 students receive a score of 97 or higher, what is the score at or below which student fail the course?

a.35 b.40 c.55 d.62 e.66




Okay I dont know the answer but here is the logic I used ......i dont think its correct help me where I am wrong

Mean=76
8 Students received 97 or higher
P(x>97) = 8/400
P(X>97)=2%
100-2%=98%
Since 98% of the values in the distribution lie within 3 standard deviation of the mean

Hence
97-3(s.d)=76
s.d=7

16% failed hence (100-16%)/2 = 42%+42%= 84% which lies between 1 standard deviation or 2 standard deviation for approximation i use 2

hence

76-2*7= 62 ( I subtract cause its about failing )

what do you all say? some say answer is 66?

Not sure what this is doing in a GMAT forum, but.....

98% is closer to 2 standard deviations than 3. So that would make the standard deviation equal to about 10.5. And the bottom 16% is about 1 standard deviation away from the mean. So that would be 76-10.5=65.5 or approximately 66.