Consider the length of time a student spends making a cell phone call, sending/retrieving a text message, or accessing e-mail on his/her cell phone. Let x represent the length of time, in seconds, for a single cell phone activity (call, text, or e-mail).

Here, we are interested in the sampling distribution of x, the mean length of time for a sample of size n cell phone activities.

1. Keep track of the time lengths for all cell phone activities you engage in over the next week.

2. Pool your time length data with data from other class members or the entire class so that the pooled data set has at least 100 observations. Designate someone in the group to calculate the mean and standard deviation of the pooled data set.

3. Devise a convenient way to choose random samples from the pooled data set. (For example, you could assign each observation a number beginning with “1” and use a random number generator to select a sample.)

4. Choose a random sample of size n = 30 from the pooled data, and find the mean of the sample. Group members should repeat the process of choosing a sample of size n = 30 from the pooled data and finding the sample mean until the group has accumulated at least 25 sample means. (Call this data set Sample Means.)

5. Find the mean and standard deviation of the Sample Means data set. Also, form a histogram for the Sample Means data set. Explain how the Central Limit Theorem is illustrated in this activity.