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. (a) What is the latest day they should send the invitation to a given guest, so the guest receives the invitation on time (by on time, we mean at least seven days before the wedding) with 90% probability? (b) They forgot to send an invitation to one of the guests and ended up sending it only on May 6th. What is the probability that the guest will receive the invitation before the wedding (i.e., in 13 days or less)