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?
3. Let X be a normally distributed random variable with mean � and standard deviation �:
a. Show that
P(� Mu- 1:96� < X < Mu� + 1:96�) = 0:95:
Hint: standardize!
b. Find a value �Beta(Greek letter) such that
P(�Mu - Sigma� < X < Mu� + Beta(sigma��) = 0:95:
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