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Chapter 5 Review MDM 4U

Chapter 5 Review MDM 4U. Mr. Lieff. 5.1 Probability Distributions and Expected Value. determine the probability distributions for discrete random variables determine the expected value of a discrete random variable

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Chapter 5 Review MDM 4U

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  1. Chapter 5 ReviewMDM 4U Mr. Lieff

  2. 5.1 Probability Distributions and Expected Value • determine the probability distributions for discrete random variables • determine the expected value of a discrete random variable • ex: what is the probability distribution for results of rolling an 8 sided die?

  3. 5.1 Probability Distributions and Expected Value • ex: what is the expected value for rolling an 8 sided die? • ans: 1(⅛) + 2(⅛) + 3(⅛) + 4(⅛) + 5(⅛) + 6(⅛) + 7(⅛) + 8(⅛) = 4.5

  4. 5.2 Pascal’s Triangle and the Binomial Theorem • Determine the number of paths using Pascal’s Triangle • Grid • Checkerboard • Word grid

  5. 5.2 Pascal’s Triangle and the Binomial Theorem

  6. 5.3 Binomial Distributions • recognize a binomial experiment situation • n identical trials • two possible outcomes • independent events (constant probability) • calculate probabilities for these situations

  7. 5.3 Binomial Distributions • ex: A family decides to buy 5 dogs. If the chances of picking a male and female are equal, what is the probability of getting 3 males? • ans: using binomial probability distribution formula:

  8. 5.3 Binomial Distributions • Calculate the expected value for # of passes on 4 tests if you have a 60% chance of passing each time • Ans: E(x) = np = 4(0.60) = 2.4 • So you are expected to pass 2.4 tests • Expected value is an average  continuous • Don’t round in these situations

  9. 5.4 Normal Approximation of Binomial Distribution • Verify that a binomial distribution can be approximated by a Normal distribution • np > 5 • n(1 – p) > 5 • Calculate and σ, given the number of trials, n, and the probability, p • Use z-scores to calculate the probability of a range of data (below or above a value, or between two values)

  10. 5.4 Normal Approximation of Binomial Distribution • ex: A die is rolled 100 times. What is the probability of getting fewer than 15 sixes? • Ans: • From the z-score table, the probability is 28.1%

  11. 5.4 Normal Approximation of Binomial Distribution • ex: what is the probability of getting between 15 and 20 sixes? • ans:

  12. Review • pp. 324 – 325 #2, 3, 4ac, 7cd, 10-12

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