Does this confirm the second part of the central limit theorem?

Published by

Nov 7, 2022


Struggling with a similar assignment? Don’t know where to start? Don’t have time to work on this? Get a high-quality paper written for you from scratch – PLAGIARISM FREE, guaranteed to get you a good grade. To get started, please click on the Submit Your Instructions at the bottom of the page.

*I will attach the scriipt*
Use the link in the Jupyter Notebook activity to access your Python scriipt. Once you have made your calculations, complete this discussion. The scriipt will output answers to the questions given below. You must attach your Python scriipt output as an HTML file and respond to the questions below.
In this discussion, you will apply the central limit theorem and use principles of the Normal distribution to calculate probabilities. You will demonstrate two key parts of the central limit theorem:
The distribution of sample means is approximately Normally distributed (bell-shaped) as the sample size increases and we repeatedly draw these samples, regardless of the shape of the population distribution from which the samples are drawn.
The average of all sample means is equal to the population mean. In practice, the average of all sample means will closely approximate the population mean.
You will generate a population data set representing total precipitation (TPCP) in tenths of a millimeter using Python’s numpy module. The distribution of this data set will be skewed. This data set will be unique to each student, and therefore the answers will be unique as well. Run Step 1 in the Python scriipt to generate your unique population data.
In your initial post, address the following items:
In the Python scriipt, 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 scriipt.
What is the mean of the TPCP population data? See Step 3 in the Python scriipt.
In the Python scriipt, 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 scriipt.
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 scriipt.
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 scriipt.
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 scriipt.
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?
Remember to attach your Python output and respond to all questions in your initial and follow-up posts. Be sure to clearly communicate your ideas using appropriate terminology. Finally, be sure to review the Discussion Rubric to understand how you will be graded on this assignment.


Need Writing Help? Our writing specialists are here 24/7, every day of the year, ready to support you! Instantly chat with an online tutor below or click here to submit your paper instructions to the writing team.

More than just an assignment.

Explore Now →

Who is this homework service for?

* If you are having a really hard class and want to get through it, then this is for you.

* If you have a medical emergency or someone close to you has a medical emergency and you don’t think you’ll be able to turn your assignment on time, this is definitely a service you could use.

* You can use us if you are having a tough Professor who won’t give you the grades you deserve.

* If you have a tight work schedule and you are getting points deducted for not submitting assignments on time.

* English might not be your first language and you feel like you are being left behind in class because of it.

* If you have a large project coming up and don’t think you have enough time to get it done well, definitely reach out to us.


Super stoked you are checking us out! We would like to help you with your assignment. We just need a few things from you:

* The full assignment instructions as they appear on your school account.

* If a Rubric is present, make sure to attach it.

* Any relevant weekly readings or learning resources.

* Include any special announcements or emails you might have gotten from your Professor regarding your assignment.

* Any templates or additional files required to complete the assignment.

If your assignment is somewhat complex and you need to explain it, please don’t hesitate to reach out to me via live chat. 



Frequently asked questions

How soon can I get my paper done?

It depends with your deadline. If you need your paper completed in 3 hours, we will deliver it in that time. All you need to do is indicate your deadline in our custom order page here. Alternatively, if you are sending us your instructions via email, please be sure to indicate your deadline.

Will it be completely original? I don't want to be caught in a case of Academic Integrity Violation.

We are as paranoid as you are. Maybe even more! And we understand that the greatest sin you can commit in your academic journey is plagiarizing your academic work. To that end, we have made sure that we check and double-check our papers using high quality plagiarism detection tools such as SafeAssign and Turnitin before submitting the paper to you.

Who is my writer? Is he/she a native English Speaker?

All our writers are native English Speakers. That is not to say that ESL writers are not good, we just prefer hiring native writers because we want the very best people working on your paper. This might mean paying a little bit more for your paper as opposed to when you pay a foreign company whose writers are non-native English Speakers.

What if I need revisions? Will your charge additional for this?

Of course not! If you do happen to require a revision on your paper, our team will handle it for you free of charge. Matter of fact, we won’t rest till you are happy with your paper. So, ask for as many revisions as you need, it’s completely FREE!

Will you give me my money back if I don't like my paper?

We have very few instances where we delivered a paper that a client didn’t fall in love with. But if it so happens that you don’t like your paper for any reason whatsoever, we’ll refund your money back no questions asked.

I have more assignments after this, can you help me with those too?

Of course! And what’s even better is that we can reserve a writer permanently to work on your entire class. This comes in handy for projects which build up on each other and where you need just one writer, one writing style.

I got my order information wrong, can I change that?

Yes you can. Just reach out to our support team via email ( or live chat here and they’ll help you change the instructions.

Can I place an order via email instead of going through the order page?

Yes you can. Email Anna at, she’s in charge of our sales team. Alternatively, you can talk to our Live Chat team here and request to speak to Anna.

Trusted by Thousands of Students

Delivering quality assignments since 2007

%d bloggers like this: