The service department at a car dealership serviced 528 cars over the course of a 1 -week period. These customers were asked to complete a survey regarding their experience with the service department. Of those 528 customers who serviced their cars during the course of this week, 484 said they were very satisfied with the service they received.

a. Find and interpret a \(95 \%\) confidence interval for the true population proportion of customers who would respond that they are very satisfied with the service department at this dealership.

b. Estimate if more than \(90 \%\) of all customers will respond that they are very satisfied with the service department at this dealership \((\alpha=0.01)\).