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Binomial Settings

Binomial Settings. Sec. 8.1A. Binomial Setting (4 conditions). Each observation is either a “success” or a “failure”—only 2 categories of answers. Fixed number of observations (n). All observations are independent. Probability of success (p) is the same for each observation.

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Binomial Settings

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  1. Binomial Settings Sec. 8.1A

  2. Binomial Setting (4 conditions) • Each observation is either a “success” or a “failure”—only 2 categories of answers. • Fixed number of observations (n). • All observations are independent. • Probability of success (p) is the same for each observation.

  3. Ex: How many girls? • Only 2 outcomes—boy or girl • Fixed n = 3 children • Independent: Knowing the gender of the one child tells you nothing about the gender of the next child! • Fixed p = .5 for each observation

  4. Ex: Corrine is a 75% free throw shooter. In a key game she shoots 12 free throws and only makes 7 of them. Is this unusual? • Only 2 outcomes—Make or miss • Fixed n = 12 shots • Independent: Knowing the outcome of one basket tells you nothing about the outcome of the next basket (this has actually been studied!) • Fixed p = .75 for each observation

  5. 9 Roll a die 1000 times and count how many of each number. • Only 2 outcomes • Fixed n • Independence • Fixed p • All OK

  6. 10 Roll a die 1000 times and count how many “1”s. • Only 2 outcomes • Fixed n • Independence • Fixed p • All OK

  7. 10 Ex: Deal 10 cards from a shuffled deck and count the red cards. • Only 2 outcomes • Fixed n • Independence • Fixed p • All OK

  8. 10 Ex: Survey blood donors looking for “universal” donors—blood types “O positive” are counted. • Only 2 outcomes • Fixed n • Independence • Fixed p • All OK

  9. 10 Ex: On a 40-question AP Stats exam, count the number of times the answer was “B” • Only 2 outcomes • Fixed n • Independence • Fixed p • All OK

  10. 10 Ex: Test 5 batches of jello mix for solubility, increasing the amount of sugar each time. • Only 2 outcomes • Fixed n • Independence • Fixed p • All OK

  11. 10 Ex: Engineer chooses 10 switches from 10,000. Count the number of bad switches when 10% are bad. • Only 2 outcomes • Fixed n • Independence • Fixed p • All OK

  12. The “10 switches out of 10,000” situation is almost a binomial setting. Technically, choosing one bad switch changes the probability that the next one is bad. BUT choosing 1 switch out of 10,000 does not really change the makeup of the remaining 9999 switches (like choosing 1 card out of 52) so we say the events are independent!

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