Your son is doing athletics, and his performance varies from day to day. He wants to compete, and has asked you to help him by assessing his high jumps. His coach is also a gymnastics and mathematics teacher, and tells you that jump heights of each athlete follows a Normal distribution \(\phi_{(\mu, \sigma)}\), and that in his club, \(\sigma=3 \mathrm{~cm}\). You measure your son's high jumps 10 times, and the total is 15.7 meters. Using a neutral prior, find \(90 \%\) interval estimates for the mean jump height, \(\mu\), and for your son's next jump, \(X_{+}\).