Your friends are getting married. They have to rush to send out wedding invitations because mail delivery is delayed due to the pandemic. The time it takes for mail to be delivered follows a Normal distribution with an average of 20 days and standard deviation of 4 days. The correspondences' delivery time is independent of each other. Suppose the wedding date is set to be on May 20th.

1. Suppose they will send all the 700 invitations on April 20th. What is the probability that more than 80% of their guests receive the invitation at least seven days before the wedding?
2. If they want all the 700 guests to receive their invitations at least ten days before the wedding, with 90% probability, what is the latest day they can send the invitations?
3. Suppose that guests who receive the invitation at least seven days before the wedding have a 90% probability of attending the wedding. In comparison, guests who receive the invitation within seven days of the wedding have a 75% probability of attending the wedding. Let N be the number of people that will attend to the wedding. Can we say that N follows a binomial distribution? Explain.