The nitrous oxide (N2O) emission level of all diesel cars of a particular model has a true (population) mean of 25 (micrograms/km) and std deviation of 2. Assume that the population distribution is Normal. A random sample of these cars is taken.

a) find the probability that the sample mean emisions will be less than 23 mg/km if the sample is of (i) one, (ii) four, (iii) 100, cars.

b) explain why the three answers differ, and illustrate with a graph.

c) what difference would it make if you didn’t assume that the population distribution is Normal?