The speeds of cars passing a point on a highway are analysed by the police force. It is found that the speeds follow a normal distribution with mean 115.7 km/h and standard deviation 10 km/h.

a.) Find the probability that a car chosen at random will be travelling between 110 km/h and 120 km/h.

b.) A sample of eight cars is taken. Find the expected number of the sample that are
travelling between 110 km/h and 120 km/h.

c.) Find the probability that in the sample of eight, more than five cars are travelling
between 110 km/h and 120 km h. State the assumptions you must make.