In a recent Jeep CEO meeting, the safety department announced they believe that 46 percent of 2019 Jeep Wranglers have visited a vehicle service department for an optional floor mat safety recall...

In a recent Jeep CEO meeting, the safety department announced they believe that 46 percent of 2019 Jeep Wranglers have visited a vehicle service department for an optional floor mat safety recall replacement.  A sample of 2019 Jeep Wranglers showed that 950 of the  2,275 randomly selected Wranglers received the floor mat replacement.

a) Construct and interpret a 99 percent confidence interval for the true proportion of 2019 Jeep Wranglers who have received the floor mat replacement.

b) Use your interval to comment on the safety department's belief that 46 percent of 2019 Jeep Wranglers have received the floor mat replacement.

c) A similar floor mat recall was previously issued for the 2018 Jeep Cherokee.  The Jeep CEO wants to construct a 99 percent confidence interval for the true proportion of 2018 Jeep Cherokees who have received the floor mat replacement.  What is the smallest sample size that should be used to ensure that their margin of error will be no more than 4.5 percent?