The time to complete one lap of a 100m pool by an average swimmer is known to follow a normal distribution with a mean of 180 seconds and a standard deviation of 33 seconds. Swimmers who are able to complete the lap between 167 to 193 seconds are selected for an extended training program which trains them for the national leagues.

a) What is the probability that a randomly selected swimmer takes more than 155 seconds to complete a 100m lap?

b) Determine the 66th percentile lap time of a swimmer.

c) What is the probability that a randomly selected swimmer will not be eligible for the extended training program?

d) Swimmers who have average lap times in the bottom 17.63% of the accepted range are most likely to be selected for the national leagues. What is the maximum lap time a swimmer can have if they wish to have a good chance at making it to the national leagues?