Aardvark Auto Rental rents vehicles. Each day Aardvark Automotive Rental keeps track of whether its SUVs were returned in “failing” condition. Aardvark must use more of its resources to restore each SUV with a “failing” returned condition. Aardvark rents an average of five SUVs each day. The condition of returned SUVs is recorded for many days in which five SUVs were rented.
Download the file titled SUV Failures. It contains a scatter plot of the number of failures versus frequency. To compare the results to the binomial distribution, complete the following:
- Explain why SUV rental condition scenario can be a binomial experiment.
- Using the SUV Failure scatter plot, construct a frequency distribution for the number of failures.
- Compute the mean number of failures. The formula for the mean is as follows: ∑(x⋅f)∑f
The terms x represent the total number of failures (0, 1, 2, 3, 4, 5) and f is the corresponding frequency (number of days where xᵢ failures occurred).
Explain what the numerical result means.
- From the frequency distribution, construct the corresponding relative frequency distribution.Explain why the relative frequency distribution table is a probability distribution.Then, use Excel to create a scatter plot of the probability distribution:Select the two columns of the probability distribution. Click on INSERT, and then go to the Charts area and select Scatter. Then choose the first Scatter chart (the one without lines connecting).
- Using the frequency distribution, what is the SUV failure average? In part 3, note that the numerator in the formula for the mean is the total number of failures. The total number of trials is the denominator of the formula for the mean multiplied by 5. What does this average mean?
- The Binomial Distribution is uniquely determined by n, the number of trials, and p, the probability of “success” on each trial. Using Excel, construct the Binomial Probability Distribution for five trials, n, and probability of success, p, as the SUV failure average in part 5. Here is an explanation of the BINOM.DIST function in Excel: https://support.office.com/en-ie/article/BINOM-DIST-function-c5ae37b6-f39c-4be2-94c2-509a1480770c?ui=en-US&rs=en-IE&ad=I (Links to an external site.)
For example, In Excel
represents the probability of 7 successes out of 15 (n) trials. The 0.7 is the probability of success, p.
Using the above value of n=5 with probability of success, p, as the SUV failure average in part 5, what is the probability of at least three SUV failures?
- Using the formula for the mean of the Binomial Distribution, what is the mean number of failures in part 6 above?
- In Excel, create a scatter plot for the Binomial Distribution. The instructions for creating a scatter plot are in part 4 above.
- Use the results above to compare the probability distribution of SUV failures and the Binomial Distribution. Compare the means in parts 4 and 6, too.
- If the probability distribution of SUV failures and the Binomial Distribution differ, explain why that is so.
- Do you think the Binomial Distribution is a good model for the SUV failure scenario? Why or why not?
- How can Aardvark Auto Rental use the binomial distribution to approximate SUV failures?
- In what other scenarios can Aardvark Auto Rental use the Binomial Distribution? Explain.
Write a report that adheres to the formatting and APA expectations outlined on the Citing & APA Resources page (Links to an external site.) in the CSU-Global Writing Center. 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.
- The 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, 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 the Word document 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. Your conclusion should emanate from (be aligned with) your findings.
- Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.
- Document formatting, citations, and style should conform to the Citing & APA Resources page (Links to an external site.). A short summary containing guidelines for paper formatting, citations, and references is contained in the New Sample APA Paper (Links to an external site.). In addition, information in the CSU-Global Virtual Library under the Writing Center/APA Resources tab (Links to an external site.) has many helpful areas (Writing Center, Writing Tips, Template & Examples/Papers & Essays, and others).