Cogito
Algebra 2 · Chapter 8 · Lesson 1
Distributions and Conditional Probability
Judging how unusual a value is.
10 problems · about 20 minutes · S-ID.A.4, S-CP.A.3, S-CP.B.6
What this lesson teaches
The student uses the normal distribution and computes conditional probabilities.
- Many measurements form a bell curve around the mean.
- About 68%, 95%, and 99.7% lie within one, two, and three deviations.
- Conditional probability restricts the pool of cases.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Infinite Geometric Series: First term 10, ratio 0.5. What is the infinite sum?
Answer 20
Why 20.
Review — Series and Sigma Notation: What is the sum of 1 + 2 + ... + 50?
Answer 1275
Why 1275.
Warm Up
Straightforward practice. Get the method working first.
4 problemsMean 100, standard deviation 15. About what percent lie between 85 and 115?
Answer 68
Why About 68%.
What does conditional probability change?
Answer The pool of cases being counted.
Why It restricts the denominator.
What percent lies within one standard deviation?
Answer 68
Why The first number of the rule.
What percent lies within two standard deviations?
Answer 95
Why The second.
Build It Up
The same ideas with more to keep track of.
2 problems20 students, 8 play sport. 5 of those 8 also play music. Out of 8, how many play music?
Answer 5
Why The pool is now the 8.
Does conditioning on B change the denominator?
Answer Yes. It becomes the B cases only.
Why That is what conditioning means.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Range: Mean 50, standard deviation 5. About what percent lie between 45 and 55?
Answer 68 percent
Why About 68%.
The Wider Range: Mean 50, standard deviation 5. About what percent lie between 40 and 60?
Answer 95 percent
Why About 95%.