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. 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 any assumptions.
2. They want to send the rest of the invitations 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 finish the remaining invitations on time? (Hint: think in terms of the mean.)