Assuming Jerry and Jill play independently, what is the distribution of D? Include the name of the distribution and the values of the parameters. Show your work.

Stat 311 Quiz 2

This is an untimed quiz that must be completed and uploaded before the end of the window. This quiz is open Stat 311 notes, textbook, and homework/solutions only. All responses must be your own. If I suspect that you collaborated with other people or put down answers that match something you found on the internet, your quiz score will be zero and I will file a report with the Student Conduct office. By uploading your quiz to Gradescope, you are acknowledging that you adhered to the rules and academic conduct standards set by the

University of Washington.

  • Unless specified otherwise, to receive credit you must show your work on all computations or give brief explanations, where appropriate.

o You will be graded only on the work you show.

o Partial credit may be given when you show the process used to solve a problem, even if your answer is incorrect.

o You only need to summarize answers in sentences where specified.

  • Any probabilities or quantiles can be found using R. When you use R, be sure to include the code and output.
  • All final numerical answers should be accurate to two decimal places (nearest hundredth); however, probabilities should be reported to four decimal places, if applicable
  • All intermediate calculations that are not probabilities should be accurate to at least three decimal places.
  • Do not forget units where applicable.
  • Read each problem carefully and follow directions. Make sure you answer the question that is asked.
  • When writing or typing out your solutions, please do NOT squish all your work together. Leave space between problems and the parts of each problem. Make your answers easy to read! If we cannot easily ready your work, it will not be graded.

The quiz consists of 9 multi-part problems. Each part of every problem is equally weighted.

2Problem 1 (1 point each): A junk box in your room contains 16 old batteries, 6 of which are dead. Define the random variable X = the number of working batteries in a sample of 4 batteries from the junk box.

  1. a) Name the distribution, with specific parameter values, which can be used to model X.
  2. b) Write out the correct formula, with specific numbers substituted, to find the probability that there is at most one working battery among the four sampled batteries. Do not solve.

Problem 2 (1 point each): The table below summarizes 272 films from 2011 that have been classified into a genre and have a rating. Define the events R = Rating PG-13 and G = Comedy. Use events R and G and the table below to answer parts(a) – (d). Show your work and summarize your answers in a sentence in the context of the problem.


Genre PG PG-13 R Total

Action/Adventure 20 15 20 55

Comedy 20 22 31 73

Documentary 8 11 9 28

Drama 20 39 57 116

Total 68 87 117 272

  1. a) For a randomly selected film what is 𝑃𝑃(𝑅𝑅 ∩ 𝐺𝐺)?
  2. b) For a randomly selected film what is 𝑃𝑃(𝑅𝑅|𝐺𝐺)?
  3. c) For a randomly selected film what is 𝑃𝑃(𝐺𝐺|𝑅𝑅)?
  4. d) Are the events R and G independent? Justify your answer using an equation with all the numbers filled in.
See also  Evaluate normality using the appropriate test. In 30 words or less, report the statistical test and indicate what the results of the code reveal (including stats reference). Was the assumption violated? How can you tell? Original Answers Only

Problem 3 (1 point each): A machine operation produces bearings whose diameters are normally distributed with πœ‡πœ‡ = 4.2 mm and 𝜎𝜎 = 0.08 mm. Use R to find probabilities and quantiles, as appropriate. For any problems where you use R, be sure to include the code and R output. Summarize each answer in a sentence in the context of the problem.

  1. a) If you randomly select one bearing from this population, what is the probability that the bearing has a diameter less than 4 mm?
  1. b) What bearing diameter separates the largest 6% of diameters from among all diameters from this population?
  2. c) A randomly selected bearing from this group has a diameter of 4.25 mm. What percentile does this correspond to?
  1. d) A random sample of 20 bearings are selected from this population. What is the probability distribution for the sample mean diameter? Be sure to name the distribution and the values of any parameters.
  1. e) What is the probability that the mean bearing diameter exceeds 4.26 mm?
  2. f) Find the probability that a random sample of 20 bearings has a mean diameter of exactly 4.2 mm.

3Problem 4 (1 point each): Jerry and Jill are playing in a bowling tournament. Their scores vary as they play multiple games. Jerry’s scores, X, follow a 𝑁𝑁(πœ‡πœ‡ = 208, 𝜎𝜎 = 7) distribution. Jill’s scores, Y, vary from game to game according to a 𝑁𝑁(πœ‡πœ‡ = 200, 𝜎𝜎 = 9) distribution. Define a new random variable 𝐷𝐷 = 𝑋𝑋 – π‘Œπ‘Œ for a single game in the tournament.

  1. a) Assuming Jerry and Jill play independently, what is the distribution of D? Include the name of the distribution and the values of the parameters. Show your work.
  1. b) What is the probability that Jerry will score higher than Jill in the next game in the tournament? Summarize your answer in a sentence.

Problem 5 (1 point each): A study concluded that among people infected with Cytomegalovirus (CMV), 98.1% of tests were correctly positive, while for people not infected with the virus, 97.6% of the tests were correctly negative. We also know that 20% of people carry the virus.

  1. a) What is the probability that a randomly selected person tests negative for CMV?
  2. b) What is the probability that a randomly selected person testing negative for CMV is truly CMV free?

Problem 6 (1 point each): Define X to be the time to wait for placing an order at a drive through window and assume X follows a continuous uniform distribution between 0 and 11 minutes. Include units as appropriate.

  1. a) What is the height of the probability density function?
  2. b) Find the mean wait time for placing an order at the drive through window.
  3. c) Find the probability that the time to wait for placing an order is between 5 and 7 minutes.
  4. d) About 75% of the customers are expected to wait at most x minutes. Find x.
See also  Describe the history of the development or discovery of this compound. Does that show up in the name? Original Answers Only

Problem 7 (1 point each): The number of typos per page in a certain printing of a novel has an average of 1.2 typos/page. Let 𝑋𝑋 be the number of typos in a random selection of 7 pages and assume 𝑋𝑋 follows a Poisson distribution.

  1. a) Specify the values of any parameters for the distribution of 𝑋𝑋.
  2. b) Write out the formula, with numbers substituted, to calculate the probability that you observe at least three typos in a random selection of 7 pages, but do not solve. (1 point) 4Problem 8 (1 point each): A test consists of 32 multiple choice questions with five choices for each question.

As an experiment, you GUESS on each answer without even reading the questions. Define X to be the number of questions you get correct based on guessing and assume X follows a binomial distribution. Use this information to answer parts (a) and (b). Include units where appropriate.

  1. a) Find πœ‡πœ‡ 𝑋𝑋 .
  2. b) Which of the options below is the exact probability that you guess correctly on at least 14 questions?
  3. 1 βˆ’ βˆ‘ οΏ½32

𝑖𝑖 οΏ½ (0.2)𝑖𝑖 (0.8) 32βˆ’π‘–π‘–32


  1. 1 βˆ’ βˆ‘ οΏ½32

𝑖𝑖 οΏ½ (0.2)𝑖𝑖 (0.8)32βˆ’π‘–π‘–13


  1. βˆ‘ οΏ½32

𝑖𝑖 οΏ½ (0.2)14 (0.8)1832


  1. βˆ‘ οΏ½32

𝑖𝑖 οΏ½ (0.2)𝑖𝑖 (0.8) 32βˆ’π‘–π‘–32


  1. 1 βˆ’ βˆ‘ οΏ½32

𝑖𝑖 οΏ½ (0.2)𝑖𝑖 (0.8)32βˆ’π‘–π‘–13


  1. None of the above.

Problem 9 (1 point each): A game is played in two steps. First you flip an unfair coin with 𝑃𝑃(𝐻𝐻) = 0.6. If you get heads, you draw a marble from an Urn that has 6 red marbles and 4 blue marbles. If you get tails, you flip the coin again.

  1. a) What is the sample space for this two-step game?
  2. b) Let 𝐴𝐴 be the event the outcome has a tail. What is the probability of event 𝐴𝐴?
  3. c) Let 𝐡𝐡 be the event the outcome has a red marble. What is the probability of event 𝐡𝐡?

Β is an academic writing platform that provides students and professionals with quality services to ease their assignment challenges. With a wide range of services, the platform has become one of the leading academic writing service providers in the market due to its reliability and affordability. Below, we shall discuss some of the services which provides:

Essay Writing Service
The essay writing service provides customers with quality essays on any subject or topic they requested within a given deadline. The writers at custompaper are experts in their respective fields, and they ensure customer satisfaction by producing original content with thorough research involved backed up with strong evidence from reliable sources available online or offline. All essays come with free plagiarism reports as well as revisions if needed so that customers can trust that they are getting high-quality work for their money’s worth.

Research Paper Writing Service
This is another popular service offered by custom paper help wherein customers are assisted in conducting research papers according to their needs and requirements within specified deadlines. Writers at custom paper help have vast knowledge about various topics belonging to different disciplines such as Management, Arts & Humanities, History etc., allowing them to craft impeccable research papers every time regardless of the complexity or urgency level requested by customers. Additionally, all our research papers come along with proper citation formats which ensures customer’s safety when it comes to plagiarism issues while also helping them save time on formatting procedures thus improving overall efficiency even further!

See also  Discuss your results in each point as stated below.

Dissertation Writing Service
CustomPaperHelp also offers dissertation writing assistance for those who need it most – students preparing for graduation or professionals wanting to further refine their skills through higher education levels such as Master/PhD degrees etc, Our team of writers consists of experienced individuals having Master’s/PhD degrees themselves so you can rest assured that your dissertation will be handled expertly from the start till the end! Furthermore, we offer unlimited revisions until your complete satisfaction is achieved, along with regular checkups being done throughout the process just so everything goes according to course without any hiccups!

Editing And Proofreading Services
If you already have written an essay but want professional feedback before submitting it, then CustomPaperHelp also offers editing & proofreading services which helps in identifying & rectifying errors present in assignments like grammar mistakes, spelling mistakes, punctuation problems etc., thereby ensuring top-notch quality work, before submission takes place! We understand how important accuracy & consistency are when it comes to grading systems used at universities nowadays, so taking extra care during this phase becomes absolutely essential if good grades are desired afterward!

Coursework Help
For those who find coursework difficult due to complications of being quite technical in nature; CustomPaperHelp extends its support here too, by providing quality solutions every single time – starting from understanding concepts properly up until composing flawless answers following university guidelines closely enough making sure no loopholes remain whatsoever! Whether it’s related math problem-solving algorithms or lengthy home assignments – our expert panel has got you covered from head-to-toe leaving no stone unturned during this very crucial stage since final grades depend largely upon the success rate achieved here successfully!

Assignment Help
Assignments form an integral part of getting better scores & ultimately, a degree itself (in case pursuing a masters/PhD) – something only possible if precision is made a priority right away; otherwise, chances of failure increase exponentially over a time period detrimentally affecting performance evaluation systems later down road drastically hence stressing timely importance completion prior commencement other operations associated same project altogether consistently meeting high standards expected each situation respectively! Here too, CustomPaperHelp presents comprehensive solution package exceeding expectations beyond point offering optimal values therein ensuring maximum satisfaction reached under circumstances prevailing accordingly without fail…proving once more why people trust us implicitly without second thought whatsoever!!

Calculate your paper price
Pages (550 words)
Approximate price: -

Why Choose Us

Quality Papers

We value our clients. For this reason, we ensure that each paper is written carefully as per the instructions provided by the client. Our editing team also checks all the papers to ensure that they have been completed as per the expectations.

Professional Academic Writers

Over the years, our Acme Homework has managed to secure the most qualified, reliable and experienced team of writers. The company has also ensured continued training and development of the team members to ensure that it keep up with the rising Academic Trends.

Affordable Prices

Our prices are fairly priced in such a way that ensures affordability. Additionally, you can get a free price quotation by clicking on the "Place Order" button.

On-Time delivery

We pay strict attention on deadlines. For this reason, we ensure that all papers are submitted earlier, even before the deadline indicated by the customer. For this reason, the client can go through the work and review everything.

100% Originality

At Custom Paper Help, all papers are plagiarism-free as they are written from scratch. We have taken strict measures to ensure that there is no similarity on all papers and that citations are included as per the standards set.

Customer Support 24/7

Our support team is readily available to provide any guidance/help on our platform at any time of the day/night. Feel free to contact us via the Chat window or support email:

Try it now!

Calculate the price of your order

We'll send you the first draft for approval by at
Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

Custom Paper Help has stood as the world’s leading custom essay writing services providers. Once you enter all the details in the order form under the place order button, the rest is up to us.


Essay Writing Services

At Custom Paper Help, we prioritize on all aspects that bring about a good grade such as impeccable grammar, proper structure, zero-plagiarism and conformance to guidelines. Our experienced team of writers will help you completed your essays and other assignments.


Admission and Business Papers

Be assured that you’ll definitely get accepted to the Master’s level program at any university once you enter all the details in the order form. We won’t leave you here; we will also help you secure a good position in your aspired workplace by creating an outstanding resume or portfolio once you place an order.


Editing and Proofreading

Our skilled editing and writing team will help you restructure you paper, paraphrase, correct grammar and replace plagiarized sections on your paper just on time. The service is geared toward eliminating any mistakes and rather enhancing better quality.


Technical papers

We have writers in almost all fields including the most technical fields. You don’t have to worry about the complexity of your paper. Simply enter as much details as possible in the place order section.