EXAMPLE 9 Sometimes there is insufficient information to solve the problem

Using the same data set as in Example 8, suppose the sample size is only . Now try again to find the probability that a random sample of size vehicles will have a mean city mpg greater than 21.

Solution

The population is skewed (not normal) and the sample size is less than the minimum required to apply the Central Limit Theorem. Therefore, we have insufficient information to conclude that the sampling distribution of the sample mean is either normal or approximately normal. This is Case 3 from the Three Cases (page 401). Unfortunately, we cannot find the probability that a random sample of vehicles will have a mean city mpg greater than 21.