Name: _______Answers____________________ Geometric Distributions WS AP Statistics 1) Only 4% of people have Type AB blood. a) On average, how many donors must be checked to first find someone with Type AB blood? 1/.04 = 25 b) What is the probability that at most five people will have to be checked before first finding someone with Type AB blood? P(X < 5) - .1846 c) What is the probability that we won’t find a Type AB donor before the tenth person? P(X > 10) = .6925 d) What is the probability that out of 10 donors at least one have Type AB blood? 1 – (.96)10 = .3352 2) Cards with athlete’s pictures are prizes in a certain type of cereal. There is a 20% chance that the card has a picture of Tiger Woods on it. a) What is the probability that the first box that has Tiger’s picture is the third box that you open? P (X = 3) = .128 b) What is the probability that the first box that has Tiger’s picture is at most the third box that you open? P(X < 3) = .488 c) How many boxes of cereal can you expect to open before you first find a picture of Tiger? µ = 1/.2 = 5 d) What is the standard deviation of this distribution? σ = 4.47 3) Police estimate that 80% of drivers now wear their seatbelts. The set up a safety roadblock, stopping cars to check for seatbelt use. a) How many cars do they expect to stop before finding a driver whose seatbelt is not buckled? µ = 1/.2 = 5 b) What is the probability that the first unbelted driver is in the 6th car stopped? P (X = 6) = .0655 c) What is the probability that the first 10 drivers are all wearing their seatbelts? P(all) = .810 = .1074 d) 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. (binomial) µ = 30(.8) = 24 σ= np(1 p) 30*.8*.2 2.19 4) Suppose a computer chip manufacturer rejects 2% of chips produced because they fail pre-sale testing. a) What is the probability that the fifth chip you test is the first bad one you find? P(x = 5) = .0184 b) What is the probability that the first bad chip you find is at most the tenth chip you test? P(x < 10) = .1829 c) Find the number of chips that you expect to test before finding the first bad chip. µ = 1/.02 = 50