8 Walter and Carl both often need to travel from Location A to Location B Walter walks and his travel time is Normal with mean w minutes and standard deviation o minutes travel time can t be negative without using a tachyon beam but assume that w is so much larger than o that the chance of a negative travel time is negligible Carl drives his car and his travel time is Normal with mean c minutes and standard deviation 20 minutes the standard deviation is larger for Carl due to variability in traffic conditions Walter s travel time is independent of Carl s On a certain day Walter and Carl leave from Location A to Location B at the same time a Find the probability that Carl arrives first in terms of and the parameters For this you can use the important fact proven in the next chapter that if X and X are independent with X N 0 then X X N 1 2 0 02 b Give a fully simplified criterion not in terms of such that Carl has more than a 50 chance of arriving first if and only if the criterion is satisfied c Walter and Carl want to make it to a meeting at Location B that is scheduled to begin w 10 minutes after they depart from Location A Give a fully simplified criterion not in terms of such that Carl is more likely than Walter to make it on time for the meeting if and only if the criterion is satisfied