In the Python script, you created a histogram for the dataset generated in Step $1.$ Check to make sure that this data distribution is skewed and included in your attachment. See Step $2$ in the Python script.

What is the mean of the TPCP population data? See Step $3$ in the Python script.

In the Python script, you selected a random sample with replacement, of size $50($note that this is a sufficiently large sample$),$ from the TPCP population. What is the mean of your random sample? Does this sample mean closely approximate the TPCP population mean? See Step $4$ in the Python script.

You also selected $1,000$ random samples of size $50$ and calculated the mean of each sample. Then you stored those means into a dataframe. Check to make sure the output of this step is in your attachment. See Step $5$ in the Python script.

Review the plotted data distribution for these $1,000$ means. Does this approximate a Normal distribution? Does this confirm the first part of the central limit theorem? Why or why not? See Step $6$ in the Python script.

What is the "grand" mean and standard deviation of these $1,000$ means? Does the grand mean closely approximate $($on a relative basis$)$ the mean of the original distribution? Does this confirm the second part of the central limit theorem? Why or why not? See Step $7$ in the Python script.

Recall that your distribution of $1,000$ means is Normally distributed even though the population distribution was skewed and the grand mean closely approximates the population mean. In your follow$-$up posts to other students, review your peers' results and provide some analysis and interpretation.

Is their population distribution skewed? Is their distribution of $1,000$ sample means approximately Normally distributed? Does this confirm the first part of the central limit theorem? Why or why not?

Does their grand mean closely approximate their population mean? Does this confirm the second part of the central limit theorem? Why or why not?

Based on this discussion activity, what have you learned about the central limit theorem?