The scores on a sociology examination are normally distributed with a mean of 70 and a standard deviation of 10. If the instructor assigns As to 15%, Bs to 25%, Cs to 40%, Ds to 15%, and Fs to 5% of the class, find the cutoff points for grades A-D.

Question

I started with A:
p( Z> 0.15-70/10) and got -6.99 but that doesn't make sense since there is no z score beyond -3.4 on the normal distribution table. Someone help!

Answer 1

A ... top 15% ... approx. 1.037 s.d. above the mean ... grade of 80

B ... next 25% ... approx. 0.253 s.d. above the mean ... grade of 73

C ... next 40% ... approx. 0.842 s.d. below the mean ... grade of 62

D ... next 15% ... approx. 1.645 s.d. below the mean ... grade of 54