One of our new STAT 200 friends is getting married, and guess what? They are inviting all of us to the party! Yay!! Here is the problem, with the pandemic, the mail delivery is getting delayed quite a bit. The courier says that it takes an average of 20 days with a standard deviation of 4 days for a mail to get delivered and that correspondences' delivery time is independent of each other. Our friends are rushing to get the invitation ready to send to all of their guests. 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?