http://www.ck12.org Chapter 15. Concepts of Statistics
The exact answer is closer to 15.87%.
Example B
On your first college exam, you score an 82. After the exam the professor tells the class that the mean was a 62 and
the standard deviation was 10. What percentage of the class did better than you?
Solution:An 82 is 20 away from the mean so is 2 standard deviations from the mean. Therefore, this question is
asking for the percentage of students that are above +2 standard deviations above the mean.
In future statistics courses you will learn how to create the equation for this distribution and then transform it
to standard normal. For now, you can use the fact that your score was exactly 2 standard deviations above the
mean. Or, you can calculate the probability using the actual numbers.
- normalcdf(2, 1E99, 0, 1) = 0.022750 or 2.750%
- normalcdf(82, 1E99, 62, 10) = 0.022750 or 2.750%
2.75% of the class did better than you on the exam. Even though you seemed to score a B-, the professor would
probably note that you were near the top of the class and adjust grades accordingly.
Example C
The quality control technician of a widget making factory observes that widgets that are three standard deviations
too large or three standard deviations too small from the precise widget size are unusable. What is the probability of
producing a usable widget?
Solution: This question is essentially asking for the area between -3 standard deviations and positive 3 standard
deviations. The empirical rule says this should be 99.7%. Use the normalcdf function to find the exact value.