An oil change shop advertised to change oil within 15 minutes. Based on the data collected on a typical day, what is the probability that oil change will take 15 minutes or less time? Based on the data, do you think the business claim is valid? Explain why or why not.
What data?
To calculate the probability that an oil change will take 15 minutes or less, you need to know the total number of oil changes done in a day and how many of them took 15 minutes or less. Let's assume that the shop performs 100 oil changes in a day, and out of those, 85 were completed within 15 minutes.
To calculate the probability, you can use the formula:
Probability = Number of desired outcomes / Total number of possible outcomes
In this case, the desired outcomes are the oil changes that took 15 minutes or less, which is 85. The total number of possible outcomes is the total number of oil changes performed in a day, which is 100.
So, the probability of an oil change taking 15 minutes or less is:
Probability = 85 / 100 = 0.85
This means that there is an 85% chance that an oil change will be completed within 15 minutes or less, based on the data collected.
Now, let's evaluate whether the business claim is valid or not. If the shop advertised that oil changes will be completed within 15 minutes, and based on the data, there is an 85% chance that an oil change will take 15 minutes or less, then it can be concluded that the business claim is valid. The data supports the claim that the shop can perform oil changes within the advertised time frame.
However, it's important to note that this calculation is based on the data collected on a typical day. Factors such as variations in workload, complexity of oil changes, and unforeseen circumstances can affect the actual time it takes to complete an oil change. So while the probability suggests a high likelihood of completing oil changes in 15 minutes or less, individual cases may vary.