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 * Aim:** How do we use Bernoulli's Theorem to solve problems involving "at most" and "at least"?

At the end of this lesson, you will be able to...
 * 1) investigate the meaning of "at least" and "at most"
 * 2) express //at least// and //at most// Bernoulli experiments as the sum of the appropriate probabilities
 * 3) solve Bernoulli problems involving //at least// and //at most//

Today's lesson builds upon yesterday's lesson. We will still use Bernoulli (binomial distribution) to solve.

Answer these two questions 1. What does "at least mean"? 2. What does "at most" mean? 3. Write the formula for "at least' and 'at most'?

This is for "at least" and "at most". Notice how he lists his variables first, then he uses the formula.

media type="youtube" key="THcbQvmsPio" width="425" height="350"

Find the probability that when nine dice are tossed,5 will show up on at most 7. (Ans: 0.9999954355)
 * Classwork:** Answer the following problem. Be sure you set up your variables first.


 * Homework:** Answers numbers 3 - 9, 18, 19, 20

[|At_Least_At_Most.JPG]


 * Answers:**

[|A-At_Least_At_Most.JPG]


 * Journal entry:** How are the phrases"at most three days" and "at least three days" different? How does this impact upon a Bernoulli experiment?