From a random sample of 60 buses, the public transport office of the city of Montreal has calculated the average number of passengers per kilometer, the value is 4.1. Of studies Previously, the standard deviation of the population is 1.2 passengers per kilometer.

a) Find the standard error of the mean. (Suppose the bus fleet is very large.)

b) Construct a 95% confidence interval for the mean number of passengers per kilometer for the population.