EXAMPLE 9 Constructing and interpreting a prediction interval for a randomly selected value of for a given

Construct and interpret a 95% prediction interval for the number of text messages sent by a randomly selected 20-year-old.

Solution

The requirements for the prediction interval are the same as for the confidence interval, so we know from Example 8 that the requirements for constructing the prediction interval are met. Using the values obtained in Example 8, we calculate the lower and upper bounds as follows:

We are 95% confident that the number of text messages sent by a randomly selected 20-year-old lies between 24.3947 and 36.8053.