No. of Failures

Frequency

Option #2: Rental Condition

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:

1. Explain why SUV rental condition scenario can be a binomial experiment.

2. Using the SUV Failure scatter plot, construct a frequency distribution for the number of

failures.

3. 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 xᵢfailures occurred).

Explain what the numerical result means.

1. 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).

2. 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?

3. 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-4be294c2-509a1480770c?ui=en-US&rs=en-IE&ad=I

For example, In Excel

=BINOM.DIST(7,15,0.7, FALSE)

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?

7. Using the formula for the mean of the Binomial Distribution, what is the mean

number of failures in part 6 above?

8. In Excel, create a scatter plot for the Binomial Distribution. The instructions for

creating a scatter plot are in part 4 above.

9. 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.

Requirements:

1. The paper must be written in third person.

2. 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.

3. Include a title page, introduction, body, conclusion, and a reference page.

4. 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.

5. 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.

6. 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.

7. Include any tables of data or calculations, calculated values, and/or graphs

associated with this problem in the body of your assignment.

8. 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).

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