Aardvark’s Rental Condition

Introduction 

This paper compares the data of SUV failures (from Aardvark Auto rental company) to the results of a Binomial distribution calculated using excel. The paper further explains why SUV rental condition can be classified under a binomial experiment, as well as generates numerical results of the mean of the probability distribution, mean of the binomial distribution and SUV failure average using the availed data and explains their implications. Towards the end of the paper, the writer explains the differences between the probability of the distribution of the SUV failures and the Binomial distribution. Other than these, the paper discusses how the Binomial distribution can be used to approximate SUV failure and also gives other applications of this statistics tool. 

No. of Failures Frequency 

Binomial Experiment 

The SUV rental condition scenario is a binomial experiment because there are a fixed number of trials of five SUV per day. Also, each trial is independent and does not rely on one another. This implies that the status of the vehicle that returns at the end of the day is not affected by another. The number of trials recorded can also be categorized into two categories (failure or success) based on the number of failures (Hayes, 2019) . Lastly, the probabilities of the trials remain the same throughout the process of studying. No matter the number of frequencies, the probability of the vehicles returning in a faulty state is ½ for each trial. 

Mean Number of Failures 

A 3. The mean number of failures. 

Mean = ∑(x ⋅ f)/∑f 

∑ (x ⋅ f) = 0+1+2+3+4+5= 15 

∑ f = 25+23+2+18 = 68 

15/68= 0.22 This numerical value implies that if an average of five vehicles are hired per day by Aardvark, after a given period of time, about 0.22 of them are returned in a failing condition. 

Relative Frequency 

The relative frequency distribution table is a probability distribution because it indicates the total number of observations related to a specific class of values, which are associated with the probable distribution of these occurrences. Below is a scatter plot, which represents Aardvark’s SUVs pattern. 

The SUV failure average = ∑ (total number of failures)/∑trials 

∑ ∑ (total number of failures) = 15 

∑ trials = 68 x 5= 340 

= 15/340 = 0.04 

The numerical value represents the SUV failure average of 0.04. This implies that there is a probability of 0.04 success rates (vehicles returning without failing conditions). 

Binomial Distribution 

Using the formula, BINOM.DIST (A2,A3,A4,FALSE), the probability of exactly 3/5 SUV failures is 0.001. 

The mean number of failures (mean of binomial distribution) = μ = n x p 

Where n= the number of trials p= the probability of success 

μ= 0.001 x 5 

=0.005 

This value suggests that the number of failures when 5 trials of SUV vehicles are considered is on an average of 0.005. 

Data for a scatter plot of four hundredth vs vehicle failure 

Scatter plot of four-hundredth vs failing vehicles 

The probability distribution of SUV failures differs from the Binomial distribution probability because it is from actual datafile while the latter is from theoretical outcomes. More accurate data from the data file gives a regular distribution (scatter graph) while the theoretical data obtained using theoretical assumptions give an irregular distribution (Krishnan, 2015) . The mean of the binomial distribution (0.005) is different and smaller than the mean number of failures (0.22). Unlike the SUV distribution, the fact that that the probability of failures in binomial distribution changes significantly within the five trials implies that the assumptions (conditions) of the binomial distribution are fulfilled. 

The binomial distribution is an important or good model for the SUV failure scenario because it shows two possible distinct outcomes, which entail SUV vehicle returning in a faulty condition or in a good shape (Holmes, 2017) . Consequently, it allows for the computation of the probability of observing a specific number of SUV vehicle failures when the process of five vehicles hired per day is repeated several times (Krishnan, 2015). Aardvark company can approximate SUV failures using binomial distribution by first checking the skewness of the distributions. This can be done by checking the values of p and n to ensure that the values np and n(1-p) are greater than or equal to ten. The higher the value of these variables, the easier it is to approximate the SUV failures. Aardvark can also use the binomial distribution to hire competent drivers through evaluating or approximating their possibility to cause or not to cause accidents. This would fit in a binomial distribution because it entails only two possible outcomes. Besides, the activity would be repeated several times, thus n would be the number of trials carried out. 

Conclusion 

In conclusion, as much as binomial distribution entails theoretical variables, it is a better model than the other statistical approaches that use accurate data because it gives room for making two concurrent observations of probability. However, before using a binomial distribution, certain conditions such as each successive trial must be statistically independent, the possibility of success or failure and the repeat of the process severally must be adhered to. Additionally, the transformed binomial data from excel demonstrate that binomial distribution gives more closely approximate normality than raw or accurate data. 

References 

Hayes, A. (2019). What Are the Odds? How Probability Distribution Works. 

Holmes, A. I. (2017). Introductory business statistics. . Houston, TX: OpenStax. 

Krishnan, V. (2015). Probability and random processes. . John Wiley & Sons.