Additional Topics for Exam 2 Week 6, Wednesday

Is the Binomial Model Appropriate? Situation #1: “How likely is it that in a group of 120 the majority may have Type A blood, given that Type A is found in 43% of the population?” Binomial Is Appropriate: n=120, p=43% X = # of people with type A out of 120 Independent

Is the Binomial Model Appropriate? Situation #2: “We roll 50 dice to find the number of times a six appears” Binomial Is Appropriate: n=50, p=1/6 X = # of sixes out of 50 rolls Independent

Is the Binomial Model Appropriate? Situation #3: “We roll 50 dice to find the distribution of the number of spots on the faces” Binomial Is Not Appropriate: For each trial, we’re not recording whether an event happens or not (situation #2 – we roll a six or we don’t). There are more than two possibilities for each trial.

Is the Binomial Model Appropriate? Situation #4: “We deal a card from a deck. Put it back into the deck and shuffle. Deal another card from the deck. Do this 5 times. How likely is it that we picked 5 hearts?” Binomial Is Appropriate: n=5, p=1/4 X = # of hearts out of 5 picks Independent

Is the Binomial Model Appropriate? Situation #5: “We deal 5 cards from a deck and get all hearts. How likely is that?” Binomial Is Not Appropriate: The chances of getting a heart changes as each heart is dealt. P[success]=p has to be the same for every trial in order for it to be Binomial.

Is the Binomial Model Appropriate? Situation #6: “A company realizes that about 10% of its packages are not being sealed properly. In a case of 24 packages, is it likely that more than 3 are unsealed?” Binomial Is Appropriate: n=24, p=10% X = # of packages that are unsealed out of 24 (Only holds if we assume Independents)

Is the Binomial Model Appropriate? Situation #7: “We sample people one at a time until we find five people with blood type A ” Binomial Is Not Appropriate: We don’t have an exact number of trials (n).