The average speed of a random vehicle on a specific 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)

Calculate the probability that a random vehicle has an average speed lower than 101.60 km / h.

b)

Calculate the probability that a random vehicle has an average speed higher than 75.97 km / h.

c)

We examine the average speed of 100 cars. Calculate the probability that the average speed of these cars will be over 83.67 km / h.