EXAMPLE 8 Finding two symmetric sample mean values using the Central Limit Theorem for Means

Refer to Example 7. If we take samples of size , find the two symmetric values of that contain the middle 95% of sample mean city mpg values.

Solution

Here, we use the instructions from the Finding Percentiles for Any Normal Distribution portion of the Section 6.5 Step-by-Step Technology Guide on page 380. We have and . We want the middle 95% of sample means, so we ask the TI-83/84 calculator to give us the sample mean with 2.5% to the left of it and the sample mean with 97.5% to the left of it, as shown in Figure 10. We get as the 2.5th percentile of sample means and as the 97.5th percentile of sample means. These are the two symmetric values of the sample mean that contain the middle 95% of all sample mean city mpg values.