Two swimmers, Alice and Brenda, are training for a 200m freestyle event. Alice’s lap times, in seconds, are normally distributed with mean 42 and variance 4. Brenda’s lap times, in seconds, are normally distributed with mean 43.5 and variance 6. The lap times for Alice and Brenda are independent. Before their heat, they each swim one warm-up lap.
Find the probability that Brenda’s time for the warm-up lap is less than Alice’s.
The final race consists of 50 laps. Assuming that they both start simultaneously and all lap times are independent,
find the probability that Alice beats Brenda in the race by more than 100 seconds.