Adjusting a Normal Curve & Mean, Median, Mode Question

[geekily]

Sabino took the ACT in 2003 and received a composite score of 22. If the mean and standard deviation for that year were, respectively, 20.8 and 4.8, what percent of all the students who took the exam scored better than him?

I drew out a normal curve and put the mean, 20.8, in the middle, which is the 50th percentile. Then I divided each side into 4 pieces like my teacher showed us, inscreasing each section on the right by 4.8 each time and decreasing by 4.8 on the left. The problem is, though, is that the last section on the right would end up being 40, and the highest possible ACT score, I believe, is 36. What does that mean for my curve, and how do I adjust to factor it in?

Oh, and there's one more I can't figure out:
Which of the following situations are possible regarding the mean, median, and mode for a set of data? Give examples.
a. mean < median < mode
b. mean = median < mode

Now, for the first one, for example, right away I can think of an example where it doesn't work, like if you use 1, 2, and 3 for mean, median and mode. That doesn't mean that there's not another combination of numbers that it would work for, though. How do I go about this one?

Thank you so much for any help you can give me!

 

[galactus]

#1:

\(\displaystyle \frac{22-20.8}{4.8}=0.25\)

Looking this up in the z-table, we find the corresponding value is 0.5987.

Therefore, 1-0.5987 scored better than he did.

 

[geekily]

Thanks for the reply! We have gone over z-score in class, but we haven't talked about z-tables. So, a z-score of 0.25 puts him between 1 and 2, so between the 51th and 84th percentile, which would mean that somewhere between 26 and 49% of all students scored better than him, right? I don't know how to narrow down that percentage, though.

Thank you for your help! Any ideas on the second one?