1000 Ants were captured from a colony of N ants were radioactively tagged and then released back into the colony. After 10 days, allowing for the tagged ad untagged ants to be well mixed, a sample of 321 was captured. Of these 321 ants it was discovered that 89 had been tagged.
Proportion of tagged ants in sample of 321
Proportion (p)= 89/321= 0.2772
90% Confidence interval for the proportion of tagged ants in colony using formula
ρ-z √(p(1-p)/n)

Question

1000 Ants were captured from a colony of N ants were radioactively tagged and then released back into the colony. After 10 days, allowing for the tagged ad untagged ants to be well mixed, a sample of 321 was captured. Of these 321 ants it was discovered that 89 had been tagged. 
Proportion of tagged ants in sample of 321
Proportion (p)= 89/321= 0.2772
90% Confidence interval for the proportion of tagged ants in colony using formula 
ρ-z √(p(1-p)/n) < π< ρ+z √((p(1-p))/n)
(0.2362, 0.3184)
Using this confidence interval, find a 90% Confidence interval for N, the number of ants in the colon