Terry and Tina are middle distance runners for their school's track team. Terry's time A in the 400-meter race on a randomly selected day is approximately Normally distributed with a mean of 66 seconds and a standard deviation of 0.9 seconds. Tina's time B in the 400-meter race on a randomly selected day is approximately Normally distributed with a mean of 65 seconds and a standard deviation of 1.1 seconds
Assume that A and B are independent random variables.
a) Find the probability that Terry beats Tina in the 400-meter race on a randomly selected day. Show work.
b) Find the probability that Tina beats Terry in the 400-meter race by at least 1 second on a randomly
selected day. Show work.