1. A large video rental chain recently decided to change its rental policy, allowing an unlimited
return date instead of requiring that movies be returned the next day. The marketing
team reasoned that this would greatly increase the popularity of their stores, and also that
80% of people would return their movies within 2 days regardless.
a. Suppose that that a specific store has 5 copies of “The Princess Bride”, and rents
them all on a Saturday. What is the probability that all 5 copies are returned by
Monday?
b. The same store rented 250 movies in total that Saturday. What is the probability that
at least 75% of these movies were returned by Monday?
2. A popular casino in Windsor estimates that the chance that someone sitting at one of their
Black Jack tables has a 0.35 probability of winning a given hand. Assume that all games
played are independent.
a. Isaac decides to play until his first win, and bets $50 per game. When he wins, he
will win $100. What is Isaac’s expected net gain/loss from this strategy?
b. Suppose the casino has 100 people playing the same strategy as Isaac. What is
the probability that the casino sees no net gain from these 100 people (that is, that
it sees a net gain of zero or smaller)? Hint: recall that the variance of a geometric
random variable is (1 p)=p2:
3.
1.5 million Canadians participated in a real-time interactive IQ test. Viewers took the test
in the comfort of their own homes, on the internet or with pen and paper, while seven
teams – tattoo artists, millionaires, fitness instructors, surgeons, mayors, talk jocks and
celebrities – exercised their grey matter in CBC’s Toronto studio. Suppose that 25% of
Canadians scored above average (that is, scoring 110 or more). You took a random sample
of n=81 individuals and recorded their IQ scores. Let bp denote the sample proportion
of individuals who scored above average.
a. What is the probability that bp lies between 19% and 22%?
b. Ninety percent of the time, the sample proportion bp is smaller than what number?
c. Would a value of bp = 0:35 be considered unusual? Justify your answer.
1 answer