A psychologist is interested in constructing a 99% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 62 of the 720 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible.

a. With 99% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between-_____and _____.

b. If many groups of 720 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About _______ percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about ______ percent will not contain the true population proportion.

Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a sample of size 87 with 51 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. C.I. =