Vehicle speed on a particular bridge in China can be modeled as normally distributed ("Fatigue Reliability Assessment for LongSpan Bridges under Combined Dynamic Loads from Winds and Vehicles," J. of Bridge Engr., 2013: 735-747).
a. If 5% of all vehicles travel less than 39.12 m/h and 10% travel more than 73.24 m/h, what are the mean and standard deviation of vehicle speed?
b. What is the probability that a randomly selected vehicle's speed is between 50 and 65 m/h?
c. What is the probability that a randomly selected vehicle's speed exceeds the speed limit of 70 m/h?