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Counting and Classification (Dr. Monticino)

Counting and Classification (Dr. Monticino). Assignment Sheet. Read Chapter 17 Assignment #10 (Due Monday April 11 th ) Chapter 17 Exercise Set A: 1,2,4,6 Exercise Set B: 1,2,4 Exercise Set C: 1,2,3,5,7 Exercise Set D: 1-3 Exercise Set E: 1,3,6 Review Exercises: 1-4,7,9,12

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Counting and Classification (Dr. Monticino)

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  1. Counting and Classification(Dr. Monticino)

  2. Assignment Sheet • Read Chapter 17 • Assignment #10 (Due Monday April 11th ) • Chapter 17 • Exercise Set A: 1,2,4,6 • Exercise Set B: 1,2,4 • Exercise Set C: 1,2,3,5,7 • Exercise Set D: 1-3 • Exercise Set E: 1,3,6 • Review Exercises: 1-4,7,9,12 • Quiz 9 will be over Chapter 16 and possibly part of Ch 17 • Test 2 over Chapters 13 - 18 is scheduled for April 13th

  3. Overview • Counting and classification • Distribution of sum • Examples

  4. Counting and Classification • The number of times that a particular event occurs as the outcome of a chance process is often the focus of study • Number of times that a head occurs out of 10 flips of a coin • Number of times that an ace occurs out of 30 rolls of a die • Number of females born out of 500 births • In these cases, the experiment can be regarded as a process producing 1’s and 0’s • 1’s occurs when the event of interest happens • Sum of the 0’s and 1’s that occur is the number of times that the event occurs

  5. Normal Approximation • Expected sums are the number of times that the event of interest would be expected to happen (on average) • Observed sums are usually within 2 to 3 SE’s away from the expected sum • When the number of draws is large, the distribution of the (observed) sum is approximately normal with mean equal to the expected sum and standard deviation equal to the standard error

  6. Flip fair coin N = 30 Flip fair coin N = 10 Flip fair coin N = 1 Flip fair coin N = 100 Normal Approximation

  7. Example • What is the probability that 60 or more heads come up out of 100 flips of a fair coin • Determine model • Classify • Find EV of one repetition • Find EV of sum • Find SD of one repetition • Find SE (SD of sum) • Use normal approximation to find probability • Find appropriate standard unit values

  8. Example • What is the probability that 80 or more aces come up out of 400 rolls of a fair die • Determine model • Classify • Find EV of one repetition • Find EV of sum • Find SD of one repetition • Find SE (SD of sum) • Use normal approximation to find probability • Find appropriate standard unit values

  9. Example • What is the probability that less than 1000 females are born out of 2500 births • Determine model • Classify • Find EV of one repetition • Find EV of sum • Find SD of one repetition • Find SE (SD of sum) • Use normal approximation to find probability • Find appropriate standard unit values (Dr. Monticino)

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