Chapter 17 – AP Statistics Bethany Warner

VOCAB BERNOULLI TRIALS IF… 1) There are two possible outcomes. 2) The probability of success is constant 3) The trials are independent GEOMETRIC PROBABILITY MODEL: A geometric model is appropriate for a random variable that counts the number of Bernoulli trials until the first success BINOMIAL PROBABILITY MODEL: A Binomial model is appropriate for a random variable that counts the number of successes in a number of Bernoulli trials. SUCCESS | FAILURE CONDITION: For a normal model to be a good approximation of a binomial model,, we expect at least 10 successes and 10 failures.

MAIN CONCEPT/FORMULAS: BERNOULLI TRIALS GEOMETRIC MODEL BINOMIAL MODEL Applies to situations when you count until your first success 𝜇= 1 p 𝜎 = 𝑞/ 𝑝 2 Applies to situations when you count the number of successes 𝜇=np 𝜎= 𝑛𝑝𝑞

FORMULAS: in the calculator. After 2nd; vars BINOMCDF BINOMPDF Used for an exact number of trials For “or”, “at least”, and cumulative successes ( # trials, % success, # times you want success )

#29 Police estimate that 80% of drivers now wear their seatbelts. They setup a safety roadblock, stopping cars to check for seatbelt use. How many cars do they expect to stop before finding a driver whose seatbelt is not buckled? What‘s the probability that the first unbelted driver is the 6th car stopped? What‘s the probability that the first 10 drivers are wearing their seatbelts? If they stop 30 cars during the first hour, find the mean and standard deviation of the number of drivers expected to be wearing seatbelts. If they stop 120 cars during this safety check, what‘s the probability they find at least 20 drivers not wearing their seatbelts?

#31 Scientists wish to test the mind-reading ability of a person who claims to “have ES.” they use 5 cards with different and distinctive symbols (square, circle, triangle, line, squiggle). Someone picks a card at random and thinks about the symbol. The “mind reader” must correctly identify which symbol was on the card. If the test consists of 100 trials, how many would this person need to get right in order to convince you that ESP may actually exist?