The average speed for a random vehicle on a certain stretch is assumed to be normally distributed with an expectation of 84 km/h and a standard deviation of 11 km/h. We assume independence between the vehicles.

a. What is the probability for a random vehicle having an average speed that is lower than 101.60 km/h?

b. Calculate the probability for a random vehicle having an average speed higher than 75.97 km/h

c. We examine the average speed for 100 cars. Calculate the possibility that the average speed for these cars are over 83.67 km/h