In a poll to estimate presidential popularity, each person in a random sample of 1,230 voters was asked to agree with one of the following statements:

1. The president is doing a good job.

2. The president is doing a poor job.

3. I have no opinion. A total of 575 respondents selected the first statement, indicating they thought the president was doing a good job.

a. Construct a 99% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

b. Based on your interval in part (a), is it reasonable to conclude that a majority of the population believes the president is doing a good job?