Question: A major video rental chain recently decided to allow customers to rent movies for three nights rather than one. The marketing team that made this decision reasoned that at least 70% of the customers would return the movie by the second night anyway. A sample of 500 customers found 68% returned the movie prior to the third night.
a. Given the marketing team's estimate, what would be the probability of a sample result with 68% or fewer returns prior to the third night?
b. Based on your calculations, would you recommend the adoption of the new rental policy? Support your answer with statistical reasoning and calculations.