Mallory has discovered that the amount of time it takes for a dollar bill to turnaround is distributed N(19,81) in weeks. Sadly she absolutely refuses to tell Patrick, and so Patrick is forced to sample random dollar bills to try to figure our the mean for himself.
Assume Mallory is correct, and that Patrick plans on sampling 9 dollars.
A) What is the probability that Patrick's sample average will be more than 20?
B) Patrick took his sample and his average was 22.57. Now what is the probability that his sample average is more than 20?
C) What is the probability that the true average turnaround time is greater than 20?