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In \(2004,17 \%\) of Florida's population was 65 and over (Source: U.S. Census Bureau). What is the probability that a randomly selected Floridian is 65 or older?

Short Answer

Expert verified
The probability is 0.17.

Step by step solution

01

- Convert Percentage to Decimal

First, recognize that the percentage needs to be converted into a decimal format for probability calculations. To do this, divide the percentage by 100. For example, to get the decimal form of 17%, compute \( \frac{17}{100} \).
02

- Simplify the Fraction

Simplify the fraction \( \frac{17}{100} \) to get the decimal form. This simplifies to 0.17.
03

- Interpret the Result

Recognize that the decimal form 0.17 represents the probability that a randomly selected Floridian is 65 or older.

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Key Concepts

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

percentage to decimal conversion
Understanding how to convert percentages to decimals is essential for various mathematical calculations, including finding probabilities.
Percentages represent a part of 100, so converting them to decimals involves dividing by 100.
For instance, if you are given a percentage like 17%, the first step is to divide this number by 100. This means: \( 17\text{%} = \frac{17}{100} = 0.17 \)
By converting the percentage into a decimal, it makes it easier to use in further calculations and probability assessments.
Remember, the decimal form of a percentage is simpler to multiply, sum up, or integrate into other equations.
simplifying fractions
Simplifying fractions is all about making the numbers easier to work with while keeping the same value.
Once you have converted a percentage to a fraction, as we did in our example (\( \frac{17}{100} \)), check if the fraction can be simplified further.
In this case, \( \frac{17}{100} \) is already in its simplest form because 17 and 100 do not share any common factors other than 1.

Thus, the simplified fraction remains \( \frac{17}{100} \). Ensuring fractions are in their simplest form makes it more straightforward to interpret and apply them in practical situations.
interpreting probability results
Interpreting probability results enables you to understand the chances of an event occurring.
Probability is represented as a number between 0 and 1, where 0 means the event cannot happen, and 1 means the event is certain to happen.
For example, our previous computation converted the percentage of Floridians aged 65 or older into a decimal (\(0.17\)).

This means there is a probability or chance of 0.17 that a randomly selected person from Florida will be 65 or older.
In other words, this is the same as saying there is a 17% chance of picking a person aged 65 or above from the population.
Understanding these probability results helps in making data-driven decisions and assessments.

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Most popular questions from this chapter

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