The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 21 and a standard deviation of 5. The population distribution can be assumed to be normal. A random sample of these cars is taken.
a. Find the probability that sample mean fuel consumption will be fewer than 20 miles per gallon if
i. A sample of 1 observation is taken.
ii. A sample of 4 observations is taken.
iii. A sample of 9 observations is taken.
b. Explain why the three answers in part (a) differ in the way they do. Draw a graph to illustrate your reasoning.