Curve Regions
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice reading probability statements and shading the correct region on a normal curve. Students work with five normal-distribution diagrams and are asked to mark given values on the horizontal axis, then shade the region that matches each probability statement.
Some problems ask for the area to the left of a value, others ask for the area to the right, and one asks for the area between two values. This gives students a visual way to connect probability notation with the shape of the normal curve.
What Students Practice
Students practice identifying whether a probability describes a left-tail region, a right-tail region, or the area between two values. They then locate the cutoff value or values and shade the correct part of the curve.
The worksheet also reinforces that probability in a normal distribution is represented by area under the curve. Students begin to see how symbolic statements translate into a picture.
Why This Skill Matters
Before students use technology to calculate normal probabilities, they need to understand what region they are actually finding. A calculator can produce a number, but students still need to know whether that number represents the left side, right side, or middle of the distribution.
This visual skill also helps students catch mistakes. If their final probability seems too large or too small, comparing it with the shaded region can show whether they used the correct setup.
Common Challenges
Students may shade the opposite tail. Encourage them to read the inequality carefully and ask whether the values should be less than or greater than the cutoff.
Another common mistake is forgetting that a “between” probability needs two boundaries. Both values should be marked before the middle region is shaded.
How To Use It
Teachers can use this worksheet before introducing normal-distribution calculator functions. It works well for guided practice, independent work, homework, or a quick visual review.
Parents and homeschool teachers can ask, “Are we looking for values below this number, above it, or between two numbers?” Once that is clear, the shading becomes much easier.
Grade Alignment
This worksheet is intended for Grade 12 Pre-Calculus students working with normal distributions. It supports visual interpretation of probability statements and prepares students for exact area calculations.
Students should already understand the shape of a normal curve and basic probability notation. After this practice, they are ready to calculate normal probabilities with technology.