Credit card ownership varies across age groups. In 2018, CreditCards.com estimated that the percentage of people who own at least one credit card is 67% in the 18–24 age group, 83% in the 25–34 age group, 76% in the 35–49 age group, and 78% in the 50+ age group. Suppose these estimates are based on 455 randomly selected people from each age group. 

a. Construct a 95% confidence interval for the proportion of people in each of these age groups who owns at least one credit card. 

b. Assuming the same sample size will be used in each age group, how large would the sample need to be to ensure that the margin of error is .03 or less for each of the four confidence intervals?