HW 7 Key
11:34 A commuter airline deliberately overbooks flights, figuring that only 75% of passengers with reservations show up for its flights. It flies small propeller planes that carry 20 passengers.
11:34 a In order to use a binomial model in this problem, what assumptions are necessary? Are these reasonable? Each event produces one of two possible outcomes (success and failure) The probability of success, denoted p, is the same for every visit The outcomes of the events are independent Yes, each person flying is a yes or no, the probability is .75, and they are independent.
11:34 b b. If the airline allows 25 passengers to book reservations for a flight, what is the probability that the flight will be oversold? Do not use the probability distribution and instead think about the mean and shape of the binomial distribution. .0625
11:34 c c. Find the probability of overbooking. Did the rough approach taken in part (b) get close enough to the right answer? .2137
11:41 A basketball player attempts 20 shots from the field during a game. This player generally hits about 35% of these shots.
11:41 a In order to use a binomial model for the number of made baskets, what assumptions are needed in this example? Are they reasonable? Each event produces one of two possible outcomes (success and failure) The probability of success, denoted p, is the same for every visit The outcomes of the events are independent You need to assume that all shots are made with 35% accuracy independently. This is plausible, yet debatable.
11:41 b b. How many baskets would you expect this player to make in the game? 20*.35 = 7
11:41 c c. If the player hits more than 11 shots (12, 13, 14, … or 20), would you be surprised? Yes, probability 0.019579
11:41 d d. How many points would you expect the player to score if all of these are 2-point shots? 7*2=14
11:41 e e. If this player randomly takes half of the shots from 3-points range and half from 2-point range and makes both with 35% chance, how many points would you expect the player to score? 17.5