Mathematics
Grade 4
15 min
Find probabilities using the normal distribution
Find probabilities using the normal distribution
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the different sections of a normal distribution bell shape.
Represent the probability of landing in a section as a fraction.
Find a common denominator for two probability fractions with unlike denominators.
Add fractions with unlike denominators to find the total probability of two or more sections.
Subtract fractions with unlike denominators to compare the probabilities of two sections.
Explain that the total probability of all sections in the bell shape adds up to 1 whole.
Have you ever played a beanbag toss game where it's easiest to hit the middle? 🎯 Let's see how fractions can help us figure out the chances!
We are going to learn about a special shape called the Normal Distribution Bell Shape, which shows us the chances of things...
2
Key Concepts & Vocabulary
TermDefinitionExample
Normal Distribution (The Bell Shape)A special curve that is high in the middle and low on the sides. It shows that the result in the middle is the most likely to happen.If we measured the height of all 4th graders, most would be near the average height (the middle of the bell), and very few would be super tall or super short (the sides of the bell).
ProbabilityThe chance of something happening. We will write probabilities as fractions.The probability of a coin landing on heads is 1/2.
SectionA part or a piece of the Bell Shape. Each section has its own fraction to show its probability.The very center section might have a probability of 1/3, while a section on the side might have a probability of 1/8.
Unlike DenominatorsWhen two fractions have different bottom numbers...
3
Core Formulas
Total Probability Rule (Addition)
P(A \text{ or } B) = P(A) + P(B) = \frac{a}{b} + \frac{c}{d}
To find the total probability of being in Section A OR Section B, you add their fractions. Remember to find a common denominator before you add!
Probability Difference Rule (Subtraction)
P(A) - P(B) = \frac{a}{b} - \frac{c}{d}
To find out how much more likely Section A is than Section B, you subtract the smaller fraction from the larger fraction. You also need a common denominator here!
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A bell shape has a center section with probability 5/12. The section to its left has probability 1/4. The section to its right also has probability 1/4. What is the total probability of landing in ANY of these three sections?
A.7/20
B.7/12
C.11/12
D.9/12
Challenging
A game designer says a bell shape is split into three sections with probabilities 1/2, 1/3, and 1/6. Do these three sections make up the entire bell shape? (Hint: The whole shape must equal 1).
A.Yes, because 1/2 + 1/3 + 1/6 = 1.
B.No, because the total is less than 1.
C.No, because the total is more than 1.
D.It's impossible to tell.
Challenging
The total probability of landing in Section A OR Section B is 7/10. The probability of landing in Section A alone is 1/5. What is the probability of landing in Section B?
A.9/10
B.5/10
C.6/5
D.8/15
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free