The most commonly chosen answer was 75%. This was probably based on the information about ISU, the top 25% scored 27 and higher, so the bottom 75% must have scored lower. But the question is about the percentage of students that take the ACT, not the percentage of students accepted into ISU.
For this we need to know how many standard deviations away from the mean 27 is, in other words the z-score. z =(27-18)/6 = 1.5.
The percent of students that scored below 27, is the same as on a Standard Normal model, the percent of a z-score being less than 1.5.
There are multiple ways we can find this information. One would come from the diagram I saw a couple of groups posted on the wiki.
If you add up all the percentages from the left all the way up to 1.5 (or just do 100 - the percents to the right) you get 93.3%. So about 93% of all scores are less than a 27.
You could also use your calculator, there is a function called normalcdf().
And finally you have a table in the back of the book (something you would also have with you when you take the AP Test).
This problem can be done using the graph above or the less complicated 68-95-99.7 rule/picture.
For the ACT, 24 is exactly 1 standard deviation above the mean, and 30 is exactly two standard deviations above the mean. So we can use the 68-95-99.7 rule.
Since 95 percent of the data is between 6 and 30, that means 47.5% between 18 and 30.
Since 68 percent of the data is between 12 and 24 that means 34% is between 18 and 24.
47.5% - 34% = 13.5%.
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