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A company that offers roadside assistance to drivers reports that the probability that a call for assistance will be to help someone who is locked out of his or her car is \(0.18 .\) Give a relative frequency interpretation of this probability.

Short Answer

Expert verified
In the long run, the relative frequency interpretation of the given probability (0.18) implies that approximately 18% of the calls the company receives for assistance are to help people who are locked out of their cars. Therefore, out of every 100 calls, around 18 calls would be related to people locked out of their cars.

Step by step solution

01

Understand the probability given

We are given that the probability of a call for assistance to help someone who is locked out of their car is 0.18. This means, out of all the calls for assistance the company receives, 18% of them are for assisting people who are locked out of their cars.
02

Define relative frequency

Relative frequency refers to the proportion or percentage of data points in a certain category or event divided by the total number of data points or events considered. In this context, the relative frequency interpretation of the probability means how many calls the company receives to help people locked out of their cars out of all the calls they get, in the long run.
03

Relative frequency interpretation

Using the given probability, we can say that in the long run, if the company receives a large number of calls for assistance, approximately 18% of these calls would be for helping people who are locked out of their cars. This means that out of every 100 calls, there would be around 18 calls relating to people locked out of their cars.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Relative Frequency
Let's dive into the world of probability by exploring what relative frequency means using an everyday example. Put simply, relative frequency is a way to express how often something happens in relation to everything else. For instance, when we say that the probability of a roadside assistance call being for a lockout is 0.18, we are talking about relative frequency. This number, 0.18, translates to 18% when we think about it as a percentage.

This means if the company received, let's say, 1000 calls, about 180 of them were calls specifically for unlocking cars. This kind of interpretation helps to grasp probability as it uses numbers to represent how frequently an event happens compared to others. This approach becomes quite handy in visualizing what percentages like 18% actually imply in real-world scenarios.
Statistical Interpretation
Statistical interpretation is a powerful tool when it comes to making sense of numbers, especially in business and practical applications. Here, the 0.18 probability signifies that 18% of assistance calls involve lockouts. To get this number, statisticians collect data over time. They track every call and categorize them based on what they needed assistance with.

In the broader sense, it's like asking what does 18 out of 100 mean for a company? In simple terms, for the company providing roadside help, it means a noticeable amount of their resources and planning will center around unlocking cars. When the probability is interpreted statistically, it allows the company to strategically plan their services. For instance, they might ensure more equipment or specialists are available for lockouts, improving efficiency and customer satisfaction.
- It allows companies to anticipate needs and adjust resources accordingly - Helps in identifying trends over time which can lead to better business decisions - Provides an understanding of customer behavior, useful for service improvement
Roadside Assistance
Roadside assistance is a safety net for drivers experiencing issues while on the road. Think of it as a reliable friend you can call when your car decides to have an off day. Services include towing, flat tire changes, fuel delivery if you run out, and yes, even helping if you're locked out of your car.

The importance of roadside assistance cannot be overstated, especially when imagining the frustration of being locked outside your own vehicle. With the statistical knowledge that 18% of calls are for such lockouts, companies can ensure they offer the right balance of support services. Over time, this understanding not only helps improve service delivery but also boosts customer trust, knowing help is just a call away.

Here's why roadside assistance is vital:
  • Provides emergency support in unexpected situations
  • Enhances driver safety and confidence on roads
  • Helps in maintaining customer satisfaction through reliable service

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Most popular questions from this chapter

In a particular state, automobiles that are more than 10 years old must pass a vehicle inspection in order to be registered. This state reports the probability that a car more than 10 years old will fail the vehicle inspection is 0.09 . Give a relative frequency interpretation of this probability.

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