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Chapter 5: Problem 22

According to the American Veterinary Medical Association, the proportion of households owning a dog is \(0.372 .\) What is the probability that a randomly selected household owns a dog?

Short Answer

Expert verified
0.372

Step by step solution

01

Understanding the Problem

The problem states that the proportion of households owning a dog is 0.372. We need to interpret what this proportion means in terms of probability.
02

Proportion as Probability

A proportion is a way of expressing a part of a whole. In this context, the proportion given (0.372) directly indicates the probability.
03

Conclusion

Since the proportion of households owning a dog is 0.372, the probability that a randomly selected household owns a dog is exactly the same value, which means the probability is 0.372.

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Key Concepts

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

Understanding Proportion
A **proportion** is a mathematical concept that shows a part of a whole. It's essentially a fraction that indicates how large one part is compared to the entire set. In our exercise, the proportion is given as 0.372. Think of it like slicing a pie; here, 0.372 of the pie represents the portion of households that own a dog.
Easier yet, you can view proportion as a ratio. For every 100 households, around 37.2 of them own a dog. This gives us insight into the overall tendency and distribution within the group of interest. Proportions are commonly represented as decimal numbers, percentages, or fractions, making them very useful for analyzing data.
Households Owning a Dog
The problem specifies the proportion of **households that own a dog** is 0.372. This figure is critical as it represents the average scenario in the real world. Essentially, out of every 1,000 households, around 372 will have at least one dog.
Understanding this number helps in several ways. For example:
  • Pet store owners can predict the potential market size for dog-related products.
  • Veterinarians can estimate their customer base and stock necessary supplies.
  • Animal rights organizations can plan for resources needed for dog welfare.
The proportion reflects an important aspect of pet ownership trends in a community, influencing decisions in business, healthcare, and policy-making.
Interpreting Probabilities
**Interpreting probabilities** involves understanding chances and likelihoods. In our context, a probability of 0.372 means that there is a 37.2% chance that a randomly selected household will own a dog. The idea is simply to convert the proportion directly into a probability, making use of its integer value.
Probabilities range from 0 to 1, where:
  • 0 means the event will never happen.
  • 1 means the event will always happen.
So with a probability of 0.372, you might say there's a roughly 'one in three' chance you'll pick a household with a dog at random. This interpretation can guide decisions in uncertain situations by providing a statistical foundation to outcomes.
The Role of Random Selection
The term **random selection** implies that each household has an equal chance of being selected, without bias or patterns affecting the outcome. This concept is pivotal for fairness and accuracy. By ensuring every household has an equal chance, we avoid skewing the results.
Random selection is important for:
  • Surveys in research and polling, to gather unbiased datasets.
  • Lottery systems, ensuring fairness in draws.
  • Statistical sampling, giving a true representation of a population.
In this exercise, random selection ensures our probability calculation of 0.372 truly reflects the likelihood of any household owning a dog without prior knowledge or influence.

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