The amount of time spent by a statistical consultant with a client at their first meeting is a random variable having a normal distribution with a mean value of 60 minutes and a standard deviation of 10 minutes.
a. What is the probability that more than 45 minutes is spent at the first meeting?
b. What amount of time is exceeded by only 10% of all clients at a first meeting?
c. If the consultant assesses a fixed charge of $10 (for overhead) and then charges $50 per hour, what is the mean revenue from a client's first meeting?