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. What is the probability that the average time of invitations sent to the 20 people involved in the wedding will be lower than 19 days? List the assumptions you are making.
2. They want to send all the invitations to their STAT 200 friends today. However, the postal service office closes in 4 hours and 30 minutes. Assuming they spend an average of 1 minute to prepare each invitation, with a standard deviation of 10 seconds, what is the probability they send all the 311 STAT 200's invitations on time? (Hint: think in terms of the mean.)