Problem: Consider one way of modeling a problem. Say you have a device and in any given year, there is a 1 in 6 chance that the device will fail. One question is, “On average, how long will it be before such a device fails?” This sort of problem is what will be modeled and analyzed here.Part 1 [Excel] (Empirical Analysis): Simulate 20 repetitions of obtaining a value for , that is, roll until a 1 is rolled, record the result and repeat this 20 times. For example, if you roll , then record 4 since 4 rolls were required. You can complete this using a die or simulating using Excel, Python, or some other option, e.g., Random.org. Record your rolls and counts.Compute the mean and standard deviation of your values for . Given the modeling problem we started with, interpret the mean and standard deviation you found in terms of how many years are expected before the device fails. Excel might be used for this part as it makes the calculations, recording of data, etc. very simple. However, it is not required.Part 2 [Excel] (Theoretical Analysis - Approximations): Compute approximations to expected value, variance, and standard deviation of the random variable . See the additional notes for discussion on these computations, in brief: = the probability of rolling something other than a 1 )-times, then rolling a 1 on the th throw. Make a table for the first 20 values: , the probability that you get the first 1 in at most 20 rolls. using the first 20 values for , namely . using the first 20 terms. For this, use and then use this and the above to get a rough approximation of . using the first 20 terms.Repeat the third item of Part 1:Given the modeling problem we started with, interpret and in terms of how many years are expected before the device fails. 1 2 … 20 Totals Use this table to computePart 3 [Written] (Theoretical Analysis – Exact Computations – (Optional)): Compute the expected value, variance, and standard deviation of the random variable . See the additional notes for discussion on these computations, in brief: (Expected Value) (Variance) (Standard Deviation) Hint: For computing these without directly manipulating the infinite summations that appear in the definitions of and , let be the event that a 1 is rolled on the first throw and be the complementary event, namely, that a 1 is not rolled on the first throw. It is clear that since what is rolled after the first roll is just like starting over. It is also clear that . The Law of Total Expectation (see notes) gives: This makes it quite simple to find . A similar “trick” can be used to find , here you will use .Again, the Law of Total Expectation gives: and from this it is simple to compute .

Finer Suit Company sells suits in the US and the European Union. The company monitors its suit sales by collecting randomly chosen data from store locations throughout the US and the EU. They record list price (in dollars), sale price (in dollars), and number of days it takes to sell each suit. Data were collected from 200 suits sold in the US and 200 in the EU region. The complete data set is in the file named Suits. Managerial Report Prepare a report (see below) that summarizes your assessment of the nature of the suit market in each region. Be sure to include the following seven items in your report. Calculate descriptive statistics (mean, median, range, standard deviation, and coefficient of variation) to summarize each of the three variables for the all US suits. Use z-scores to determine if there any outliers in the data set for any of the three variables. If there are any outliers in any category, please list them and state for which category they are an outlier. If a result is an outlier, state whether it is below or above the mean. How can one use the above descriptive statistics to understand the US suit market better? Could there be any other descriptive statistics that can help one understand the US suit market better? Descriptive statistics (mean, median, range, standard deviation and coefficient of variation) to summarize each of the three variables for the all EU suits. Use z-scores to determine if there any outliers in the data set for any of the three variables. If there are any outliers in any category, please list them and state for which category they are an outlier. If a result is an outlier, state whether it is below or above the mean. How can one use the above descriptive statistics to understand the EU suit market better? Could there be any other descriptive statistics that can help one understand the EU suit market better? Compare your summary results from #1 and #2. Discuss any specific statistical results that would help Finer Suits understand its two types of businesses. Discuss any specific statistical results that would help Finer Suits understand its two types of Develop a 99% confidence interval estimate of the population mean sales price and population mean number of days to sell for US suits. What is the margin of error? Interpret your results. Interpret what each confidence intervals means. How can both confidence intervals provide useful US suit sales information? What other confidence interval would you choose to compute to obtain more information related to US suit sales? Explain why. What happens to the confidence interval as the level of confidence is increased. Develop a 99% confidence interval estimate of the population mean sales price and population mean number of days to sell for EU suits. What is the margin of error? Interpret your results. Interpret what each confidence intervals means. How can both confidence intervals provide useful EU suit sales information? What other confidence interval would you choose to compute to obtain more information related to EU suit sales? Explain why. Assume the Finer Suit Company requested estimates of the mean List Price for the US suits with a margin of error of $600 and the mean List Price of EU suits with a margin of error of $600. Using 99% confidence, how large should the sample sizes be for each one? How could the sample size formula be useful in understanding both types of suit businesses? What are some advantages of a larger sample size? Suppose a US suit has a list price of $1,500 and an EU suit has a list price of $1,200. What is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these suits? How would these two estimates be useful in this application? Write a report that adheres to the formatting and APA expectations outlined on the CSU Global Writing Center (Links to an external site.). As with all written assignments at CSU Global, you should have in-text citations and a reference page. Submit your Excel file in addition to your report. Requirements: Paper must be written in third person. Your paper should be four to five pages in length (counting the title page and references page) and cite and integrate at least one credible outside source. The CSU Global Library (Links to an external site.) is a great place to find resources. Include a title page, introduction, body, conclusion, and a reference page. The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic. The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment. The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs. Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.  

Give an example of an interval estimate of an average or proportion you may use in your daily life. For instance, you may say that you are pretty sure your average commute time is between 25-30 minutes, or you are fairly confident that between 60-65% of the population love dogs. Collect some data to see how well your intuition is working. First, does your sample data meet all assumptions necessary to construct the confidence interval of the type you need? Even if it doesn’t, construct and interpret the confidence interval. POST this is a correct example of the question:"A confidence interval is a range of values so defined that there is a specified probability that the value of a parameter lies within it. In statistics, a confidence interval is a type of estimate computed from the statistics of the observed data. This proposes a range of plausible values for an unknown parameter. The interval has an associated confidence level that the true parameter is in the proposed range.            Between driving to work and providing morning transportation for my nanny, I estimate the average amount of miles I drive per week is about 200 miles. Calculating my Confidence Interval, adding 14.8 miles to and from work are equal to 29.6 miles per workday, 7.8 miles to and from my Nanny’s house equal to 15.6 miles per workday day and altogether the daily workday mileage, including transportation for my nanny, is 45.2 miles. In addition, misc. mileage, such as trips to the grocery store, equal an average of 10 miles per work week – as the grocery store is extremely close to home. 45.2 miles four times a week is 180.8 miles per work week. 180.8 plus 10 for misc. mileage is 190.8 The amount of mileage on two my days off has been represented numerically by “0” and the other with “10” to compensate for the misc. mileage. Ending with:Mean (?): 27.257142857143Standard deviation (?): 20.947202823347Weekly Mileage Data Set:45.2, 0, 45.2, 45.2, 45.2, 0, 10Weekly MileageWeek DaysMileage Per DayMonday45.2Tuesday0Wednesday45.2Thursday45.2Friday45.2Saturday0Sunday1095% Confidence Interval: 27.26 ± 15.5(11.8 to 42.8) "With 95% confidence the population mean is between 11.8 and 42.8, based on only 7 samples." Short Styles:27.26 (95% CI 11.8 to 42.8)27.26, 95% CI [11.8, 42.8]Margin of Error: 15.5Sample Size: 7Sample Mean: 27.26Standard Deviation: 20.95Confidence Level: 95%        In personally driving these miles on a regular basis, I have all assumptions necessary to construct the confidence interval of the type that I need."