The St. Lucie County Health Department needs to estimate the proportion of all children in the county aged 19-35 months that are completely up to date with all state-recommended immunizations. The St. Lucie County Health Department found that 67% of a random sample of children in the county aged 19-35 months were completely up to date with all state-recommended immunizations. Find three different confidence intervals - one with sample size 478, one with sample size 645, and one with sample size 854. Assume that 67% of the children each sample are completely up to date with all state recommended immunizations. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary.

• When N = the margin of error for a 95% confidence interval is given by: When N =478, a 95% confidence interval is given by:
• When N =645, the margin of error for a 95% confidence interval is given by: When N =645, a 95% confidence interval is given by:
• When N =854, the margin of error for a 95% confidence interval is given by: When N =854, a 95% confidence interval is given by: